# 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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### GAP — null multidimensional array

I need to create an $n\times a \times b$ array in GAP. How do I do that fast? I tried putting ...
1answer
20 views

### GAP — GeneratorsOfRing giving a list with repeated element

I put the following code in GAP: R := Integers mod 8; and I get the answer: [ ZmodnZObj( 1, 8 ), ZmodnZObj( 1, 8 ) ] Can ...
1answer
32 views

### GAP — make an Additive Group into a Group

I have a list of vectors $\texttt{A}$ with coordinates in $\{0,1,\ldots, n-1\}$ that happen to make a group under addition. How do I make GAP understand that it is a group? One possible solution that ...
1answer
28 views

### Basis for $\operatorname{Ext}^1(M,N)$ in QPA

It is possible to calculate for two given modules $M$ and $N$ $\operatorname{Ext}_A^1(M,N)$ using the GAP-package QPA. Assume $\operatorname{Ext}_A^1(M,N)$ is n-dimensional. Question: Is there a ...
1answer
28 views

0answers
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### Computing the multiplication of elements to generate the Cayley graph of a semidirect product

I have computed a semidirect product, $s$ of $(\mathbb{Z}_5 \times \mathbb{Z}_5) \rtimes \mathbb{Z}_3$ as below and have drawn a Cayley graph for $s$ with respect to a generating set $S$. But I wanted ...
1answer
94 views

### In how may ways can we remove lines such that all dots will still be connected?

Let there be a square, connected with 9 dots and 12 lines. We can select some lines (at least 1, maximum 4) among the 12 lines, and then remove them. In how may ways can we remove lines such that all ...
1answer
75 views

### Algorithm for finding all sets that fulfill a condition?

Lets say I have a set of none-negative integers of given length $n$ where $n>0$. $$m=\left(m_1,...,m_n\right)$$ A number can appear more than once in the same set. The same set or numbers can also ...
0answers
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1answer
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### Use GAP to define finite Clifford group

I am studying the computer algebra system GAP to do some calculations about Clifford group, which is defined (cf. Lawson and Michelsohn, Spin Geometry, Princeton 1989) as followings Definition. Let's ...
0answers
84 views

### A group theoretic interpretation of Lagarias inequality

Let $G$ be a finite group, $S \subset G$ a generating set. Set $\sigma(G):=\sum_{U \subset G} |U|$, where the sum runs over all subgroups $U$ of $G$. Set $H_G := \sum_{g \in G} \frac{1}{|g|+1}$, ...
1answer
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### how to check if there is an automorphism mapping between two conjugacy class

Let $G\le S_n$ be a permutation group and suppose that $C_1,C_2$ are two distinct conjugacy classes that have the same cardinality and is represented by a permutation of the same cycle-type. My ...
1answer
101 views

### Presentations of subgroups of S6 as permutations

Computer science professor, self-taught abstract algebraist. Beginner with GAP and SAGE. Can someone show me the quickest way to, when given the description of a subgroup of S6, obtain its ...
2answers
95 views

### Subgroups of $\operatorname{GL}_2(\mathbb Z/8\mathbb Z)$

Is there some program or a location which would allow me to work and calculate with the subgroups of the group $\operatorname{GL}_2(\mathbb Z/8\mathbb Z)$?
1answer
80 views

### Identifying the group in GAP

I am defining a matrix group in GAP. I know that its a finite group, and can compute its order. Using sonata package and commands like ...
2answers
116 views

### How to solve decics like $x^{10}+100x^2+160x+64=0$ having Galois group 10T33?

Using the approach described in Smart way to solve octics like $x^8+5992704x-304129728=0$ (the method DecomPoly available in GAP) the decic quadrinomial from this ...
0answers
33 views

### Finite Fields in GAP. How to get $d$ from the finite field with $p^d$ elements?

I'm currently working in an algorithm to decompose matrices in classical standard generators. The thing is that the parameter of my main function gets a matrix m. ...
0answers
34 views

### Conjugacy Classes of Subgroups with Special Property for a Large Group in GAP

I am trying to do the following in GAP: $G$ is a given group of order $2^{19}$ and $H$ is a subgroup (but not normal) of $G$ of order $2^{15}$. My aim is to find a representative, say $A$, for each ...
0answers
41 views

### Generating words in a finitely presented group in SAGE

I'm trying to get a list of all words of length $n$ (in the word metric sense) in some finitely presented group. I have tried some very naive enumerations but it is very slow. Is there an efficient ...
0answers
27 views

### Schur Index for Quaternion Algebra

I learned form this question and this answer that Schur index in GAP can be found using LoadPackage("wedderga") the functions "SchurIndex". But I am working on the field $K=\mathbb Q (\sqrt{-39})$ ...
1answer
54 views

### Need some help in generating the group element by generator using GAP system [closed]

I am new to GAP system. I would like to generate group using presentation of group. For example, dihedral group D_{2n} with generator . Can anyone familiar with GAP system help me out with this?
1answer
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### Constructing Invertible 0-1-matrices [closed]

I am looking for effective algorithmic solutions for the following two problems: Question 1: Is there a quick way to obtain for a given $n$ the list of all integer $n \times n$ matrices having only ...
1answer
107 views

### Groups of derangements: what is known about subgroups of a symmetric group $S_{n}$ that contain only derangements (plus the identity)?

A derangement is a permutation that has no fixed points. My question is . . . What is known about subgroups of a symmetric group $S_{n}$ that contain only derangements (plus the identity)? It is ...
1answer
60 views

### GAP semidirect product

I am newbie in the GAP and in the group theory. Now I am trying to make semidirect product if GL(3,2) and GL(3,2) inversed and transposed. I use code below ...
2answers
94 views

### Galois field elements as Integers in $\mathbb{Z}$ [closed]

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....
1answer
129 views