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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What group is this? [closed]

What type of group could this be? I need help with identifying it. It is a subgroup of $S_{50}$ With the following 10 generators: a=(7, 43)(11, 42)(21, 30)(26, 32)(29, 33), b=(5, 50)(8, 20)(17, 48)(...
45 views

Find all homomorphisms from a Finite Field (using GAP)

I'm currently working with $\mathbb F_{243}$, viewing it as an additive group. I'd like to have GAP calculate all of the (additive) homomorphisms from this group to smaller groups. I've done this with ...
52 views

Real roots of a polynomial in GAP, and RootsFloat function

Is there a way in GAP to calculate the roots of a polynomial, say $x^2-2$, as real numbers? I know I can express the roots as cyclotomic numbers, but then (real) cyclotomic numbers are not ordered as ...
44 views

Wedderburn decomposition of commutative finite dimensional algebras via GAP

Let $R$ be a commutative finite dimensional $K$-algebra over a field $K$ (for example the monoid ring of a a finite monoid over a field). Assume we have $R$ in GAP. Then we can check whether $R$ is ...
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Finding all small monoids with the help of GAP

In GAP there is the command AllSmallGroups(n) to construct all finite groups of order $n$ up to isomorphism. Question: Is there a similar method (or package) in ...
40 views

Defining the Weyl group of type $D_n$ as a subgroup of Weyl group of type $B_n$ in GAP

I am looking to define the Weyl group of type $D_n$ as a subgroup of Weyl group of type $B_n$ in the software GAP. In general, one can define these groups separately. For example, let's say ...
32 views

How to best input and work with matrices over GF2 in GAP?

I am working on a problem where I have a group of matrices and a vector space of vectors, and I am looking to calculate the orbits of said group upon said vector space with GAP. Right now, I have each ...
220 views

In GAP, how can I create a group isomorphic but not equal to a given group?

Sorry if the question title is confusing. Let me try to explain my question over an example. Please consider gap> G := SmallGroup(24, 12);; Without knowing that ...
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How to construct submodules with GAP / MeatAxe?

Let $G= \langle g_1, g_2 \rangle$ be a finite group. Let $k$ be a finite field with ${\rm char}(k)=p>0$ such that $p \mid |G|$. Let the $kG$-module $M$ be a MeatAxe-module in GAP. The generators of ...
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Changing the notation of a permutation in GAP

I have written a program in GAP which has output three permutation elements. An example is (1,3,4,2),(3,5),(2,4). What I would like is that the notation for the permutations includes all numbers, even ...
52 views

Finding maximal quotient of a particular class of a group

Given a group G, how do I find the maximal 2 quotient of class 3 for that group in GAP? For example, if ...
72 views

Finding special presentations for finite groups

Let $G$ be a finite group. Call a presentation of $G$ "normalised" (I do not know whether such presentations by generators and relations have been studied before and I invented the name &...
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Outer automorphisms of extraspecial groups in GAP

Let $G_n$ be the extraspecial group of order $2^{1+2n}$. Its outer automorphism group is known to be isomorphic to the general orthogonal group $GO(2n)$. I'd like to get an explicit map of this ...
153 views

simultaneous diagonalization of set matrices

I have a set of integral square invertible symmetric matrices $A_i$ with $A_i^2=I$ (so also $A_i A_i^T=I$). The matrices commute. I'd like to map them simultaneously to a set of diagonal matrices $D_i$...
Embedding a finite group into $\operatorname{GL}_n( \mathbb{Z})$ [duplicate]
Let $G$ be a finite group. Having a concrete realisation of this finite group as a group of matrices is often helpful for calculations, which motivates the following questions. Question 1: Is there a ...