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Questions tagged [gap]

GAP (Groups, Algorithms and Programming) is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. It provides a programming language, a library of thousands of functions implementing algebraic algorithms, and large data libraries of algebraic objects. Please note that GAP Forum or GAP Support may be more suitable places for questions about GAP: see http://www.gap-system.org/Contacts/Forum/forum.html

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Galois field elements as Integers in $\mathbb{Z}$ [on hold]

In the case of $GF(3)$ its elements are gap> Elements(GF(3)); of which I get [ 0*Z(3), Z(3)^0, Z(3)]. Further, as an example, to get the integer value of Z(3), I use gap> Int(Z(3)); of which I get 2....
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2answers
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Finding elements of subset of symmetric group

I am looking for a proper subset $A$ of symmetric group $S_n$ of $n$ elements. We define set $B$ such that- Consider the symmetric group $S_n$, and for any (nonempty*) subset $A \subset S_n$, form ...
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0answers
48 views

Computing the class-preserving automorphism group of finite $p$-groups

Let $G$ be a finite non-abelian $p$-group, where $p$ is a prime. An automorphism $\alpha$ of $G$ is called a class-preserving if for each $x\in G$, there exists an element $g_x\in G$ such that $\alpha(...
2
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1answer
30 views

Possible orders of trace k elements in $SL_2(\mathbb F_q)$

As a continuation of this question I would like to ask about possible orders of trace $k$ elements in $SL_2(q)$. Here are examples which I know. When trace is zero then we have $x^2=-1$ so it means ...
2
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1answer
64 views

Constructing minimal supplements with GAP

The problem is this: Suppose we are given a finite group $G$ and a normal subgroup $N$ of $G$ which is not contained in $\Phi(G)$. Call a subgroup $H$ of $G$ a minimal supplement for $N$ (in $G$) ...
1
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1answer
24 views

Store GAP REPL representation of expression in string

I have noticed that the representation that is displayed by the GAP REPL (read-evaluate-print loop) when an expression is evaluated sometimes differs from the result of printing that same expression, ...
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0answers
31 views

Transport/flow network in GAP

How to define a transport network in GAP? I can't seem to find a single function related to transport networks or flows in general in the GAP-GRAPE manual. I'd be content with just manually adding ...
1
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1answer
94 views

Presentation of $A_5 \times \Bbb Z_2$.

I want presentation of the group $A_5\times \Bbb Z_2$ which is a group of order $120.$ I know the presentation of $A_5$ but not of product. I tried it in GAP . In GAP its Atlas name is $2\times A_5$ ...
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0answers
57 views

Elements $A\in GL_4(\mathbb{Z}_2)$ with $A^5=I, A\neq I$ by using GAP.

I need elements $A\in GL_4(\mathbb{Z}_2)$(General linear group of $4\times 4$ matrices over $\mathbb{Z}_2$ ) with $A^5=I, A\neq I.$ By using simple calculation its hard to find such types of elements....
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1answer
51 views

To find Brauer Character for the special linear group SL(2,5) in GAP.

As suggest by Alexander Konovalov I load LoadPackage("ctbllib") and them worked for symmetric group $S5$. It worked for me as ...
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1answer
44 views

Product of $e \in A/J(A)$ with an element of $J(A)$ [GAP]

I have defined a matrix algebra over the rationals, calculated its radical, and took the semi-simple coefficient using h:=NaturalHomomorphismByIdeal and $ImagesSource(h)$. Afterwards, I calculated the ...
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2answers
61 views

Brauer Character in GAP.

What is command to obtain Brauer Character in GAP? In magma, it is like ...
6
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1answer
158 views

Smart way to solve octics like $x^8+5992704x-304129728=0$

Question: How to quickly find explicit formula for roots of polynomials (solvable by radicals) like $f(x)=x^8+5992704x-304129728$? My current approach is just a brute force - not very fast and ...
1
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2answers
61 views

Linear independent subset of a set of vectors [GAP]

I'm trying to find a linearly independent subset of a set of vectors in a vector space over the rationals. Looking up "independent", "linear independence", or anything of the sort hasn't helped, since ...
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0answers
43 views

GAP Integrated Delopment Environment

Is there any fancy editor of GAP code or even some environment dedicated to it? I've been using Notepad++ for this purpose but it seems only to color the syntax. I would like to have more ...
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0answers
19 views

WedderburnDecomposition of $FG/J(FG).$

WedderburnDecomposition(GroupRing(GF(p),G)) gives complete wedderburn decomposition for semisimple group algebra $FG$ for finitie group $G$ and finitie field $F$. But if $FG$ is not semisimple then ...
2
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1answer
50 views

jacobson radical nilpotence, associative algebras.

In $Pierce, Associative Algebras$, it is mentioned that the Jacobson radical of an associative algebra $A$ is nilpotent, meaning $J(A)^k=0$ for a natural number $k$. However, my professor said that ...
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0answers
86 views

What are some nontrivial things one could do with GAP? [closed]

I'm learning algebra at the undergraduate level and came across the group theory software called GAP. Despite some googling I'm not sure what things one could do with such software that would really ...
2
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1answer
30 views

Define the image of a representation of a finitely presented group in GAP

Please note that the example below is just a baby case in which my problem occurs. Of course there is a simple workaround for my problem in this particular example, but I would like to apply this to ...
1
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1answer
44 views

Computing quotients of group by elements of its lower exponent$-p$ central series

Let $G$ be a finite $p−$group of number of generators $d$ and exponent$−p$ class $c$, that is $c$ is the smallest integer satisfying $P_c(G)=1$ in the series $$ G=P_0(G)≥...≥P_{i−1}(G)≥P_i(G)≥... $$ ...
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1answer
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Conjugacy class of a tuple in GAP

I would like to know how to obtain the conjugacy class of some tuple in GAP, or how two know if two tuples are conjugate by an element of some group (permutation group, more especifically). I know ...
4
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0answers
40 views

Conjugacy classes of stabilizer subgroups

Let $G\subseteq GL(V)$ be a complex finite reflection group. I would like to understand the stabilizer subgroups of $G$, and their normalizers. By this I mean (the conjugacy classes of) subgroups $H&...
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0answers
73 views

associates of primes in $ \mathbb{Z}[\tau]$

In $\mathbb{Z}[\tau]$, for $\tau = \frac{1+\sqrt{5}}{2},$ how do I input through GAP its primes and their respective associates? An example for their inert and split primes would be much appreciated. ...
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1answer
41 views

Network analysis of category of groups

I am taking a course in Network Analysis at my university and I would like to do something related to category theory in my home project. To be more precise, I would like to take some amount of finite ...
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0answers
51 views

Computing quotient cayley graphs in GAP

1) $X1$ is a cayley graph and a is an automorphism (an element of Aut($X1$)) of $X1$. I'm trying to compute the quotient graph $X1$/a in GAP. I tired to use the command "QuotientGraph(X1,[a]);" in GAP ...
2
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1answer
32 views

Is there a list containing regular graphs in GAP?

I'm trying to write a function in GAP (this is the first time I am using it) and I want to loop through like the "first" $1000$ non-complete, non-empty regular graphs. Do I have to construct this ...
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0answers
68 views

Identifying result from a Cayley graph in gap

I constructed a group s which is the semidirect product $\mathbb{Z}_3 \ltimes (\mathbb{Z}_5 \times \mathbb{Z}_5)$ using GAP commands as below. ...
1
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1answer
60 views

Interpreting semidirect product in GAP in terms of underlying groups

I obtained the group $G$ which is the semidirect product $(\mathbb{Z}_5 \times \mathbb{Z}_5) \rtimes \mathbb{Z}_3$ in GAP as below. ...
2
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2answers
105 views

Can graphs in GAP be obtained as a visual output

In GAP when we draw a cayley graph of a group using "CayleyGraph" command we get a list. Is there a way to visualize that cayley graph like a figure? Or else is there any other software that has the ...
3
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1answer
63 views

How to obtain elements of dihedral group in GAP

I'd like to obtain a list of all permutations contained in D_n using GAP. E.g. for D_8 I've tried the following: ...
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1answer
56 views

Semidirect product command in GAP [duplicate]

I need to type the group in GAP. Is it correct if I type as, "SemidirectProduct(ZmodnZ(3),AbelianGroup([7,7]));"? Will it recognize that AbelianGroup([7,7]) is the normal subgroup?
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2answers
105 views

Obtaining the adjacency matrix of Cayley graphs

Is it possible to obtain the adjacency matrix of a Cayley graph of $Z_3 \times Z_5$? (Manually or by using a software like GAP). Will there be a pattern for adjacency matrices of Cayley graphs for a ...
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1answer
73 views

Direct and semidirect products in GAP [closed]

Can someone please tell me the necessary codes/commands to enter the below group in GAP. Thanks a lot in advance.
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1answer
46 views

How to rename variables in GAP during the whole program?

I'd like to ask the following question. I would like to write a GAP program which does the following in general what I will now only illustrate with an example. I have entered two quiver algebras ...
2
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1answer
74 views

List of path arrows in GAP

I am using the QPA package with GAP and have the following problem: I want to, given a path $p$, obtain a list (preferably ordered) of the arrows which make up $p$. For example, if I have arrows $...
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1answer
130 views

Computing Hochschild cohomology of an algebra in GAP

I would like to calculate Hochschild cohomology of a path algebra of a quiver (modulo some relations) using GAP. Creating the quiver and its path algebra modulo relations is explained in detail in ...
2
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1answer
42 views

Choosing different term orders for Groebner basis calculations in GAP

I am using the QPA and GBNP packages in GAP to analyze path algebra quotients. I use the GBNP package for computing Groebner bases for the ideals in the path algebras, and the term orders for these ...
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1answer
37 views

Obtaining a list up to cyclic shifts in GAP

I have a list of lists in GAP, for example as follows: $L=[ [ 2, 2, 2, 2, 3 ], [ 2, 2, 2, 3, 3 ], [ 2, 2, 2, 4, 3 ], [ 2, 2, 3, 2, 3 ], [ 2, 2, 3, 3, 3 ], [ 2, 2, 3, 4, 3 ], [ 2, 2, 4, 3, 3 ], [ 2, ...
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0answers
41 views

Normal subgroup of a normal subgroup of a group is not always a normal subgroup of a group. Prove using GAP. [duplicate]

How could I show that a normal subgroup of a normal subgroup of a group is not always a normal subgroup of a group? Here is what I did. I know the Algebra system GAP, so I wrote the following ...
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1answer
43 views

Problem with hom-spaces and their dimensions in GAP

I am running the following example in GAP using the QPA package: ...
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1answer
49 views

Error while calculating automorphism of non abelian group on Gap

I am implementing the following code to calculate the automorphism of non-abelian group on Gap. ...
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0answers
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Construct S polynomial using GAP.

I am trying to write a function which would create an s polynomial when provided with two polynomials : p1 and p2. Here it is : ...
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1answer
71 views

Full projective resolutions for path algebras in GAP

I am trying to do various computations on path algebras using GAP. One such computation is obtaining projective resolutions of simples modules (and possibly other modules). The command in the GAP ...
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1answer
38 views

Is it possible to Generate a Field given both the addition and multiplication table.

So, I've been told to research a little about GAP functions related with fields, this far I can get the "standard" representation of any field with GF(p) or GF(p^r) and a representation of GF(p^r) ...
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0answers
44 views

Find H such as |Aut(ZxG)| = |Aut(ZxH)|, where G is a given finite abelian group

I am really new in GAP, please accept my apologize if my question is a simple one. I want to implement an algorithm in GAP for the next problem: Given an abelian finite group G, find the group H such ...
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2answers
456 views

How is GAP generating all subgroups?

GAP can return all subgroups of $S_4$ pretty much instantaneously: ...
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1answer
62 views

Invariant ring using GAP

How can I use GAP to find the polynomials of the invariant ring of a finite group? I calculate the invariant ring of Dihedral groups but I want to use GAP to compare it with.
2
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1answer
48 views

Special semidirect product (wreath product) in GAP

I have $G$ a finite group with a subgroup $H$ of index 7 and $C$ a cyclic group of order 2. I want to define in GAP the semidirect product $C^7 \rtimes G$ where every $g \in G$ acts on $C^7$ by ...
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1answer
92 views

In seek of a (counter)example

I am looking for an example of a finite group $G$ and a subgroup $H$ of $G$ with the following property: The number of conjugacy classes of subgroups of $G$ which are isomorphic to $N_G(H)$ is ...
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1answer
52 views

Exceeded the Permitted Memory [closed]

I have been trying to program with large matrices, but unfortunately I have been getting an error that my permitted memory has been exceeded. I have read various ways online that it is possible to ...