# 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.

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### Creating a List of permutations given a condition with GAP system [closed]

Please, I am new to GAP system and I am trying to test the following simplified form of code where I intend to test a given condition on a set of permutations and then add to the list M of the ...

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### Relations of minimal number of generators

What is the command in GAP to find the all relations of minimal generators of a finite $p$-group $G$?

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### GAP versus SageMath for branching to Lie subgroups

Which computer package is better, GAP or SageMath, for
decomposing an irreducible representation of a (simple) Lie group
$G$ into representations of a Lie subgroup. I am most interested when
...

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### Finding all $d$-dimensional indecomposable representations

Given a connected quiver algebra $A$ over a finite field $K$.
Question : Is there an effective/quick method to obtain all $d$-dimensional indecomposable representations for a fixed $d$ with a ...

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### Obtaining quiver and relations for finite p-groups

Given a finite field $K$ with $p$ elements and a finite $p$-group $G$, is there a way to obtain the quiver and relations of $KG$ with GAP (and its package QPA)?
Since $KG$ is local, the quiver should ...

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### Recovering the bimodule from the trivial extension

Given a ring $S$ with a non-zero $S$-bimodule $M$, the trivial extension of $(S,M)$ is defined as the ring $R:=T_M(S)$ with $R= S \oplus M$ with multiplication $(s,m)(s',m')=(s s', sm' +m s')$.
We ...

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### 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(...

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### Obtaining the reduced incidence algebra in QPA

Given a finite poset $P$ (we can assume it is connected), the reduced incidence algebra of $P$ is the subalgebra of the incidence algebra of $P$ consisting of functions constant on isomorphic ...

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### Algebra dimension computation in GAP

How does GAP compute the dimension of a matrix algebra over the rational numbers? I am curious about the run time.
For example, the manual https://www.gap-system.org/Manuals/doc/ref/chap62.html does ...

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### Is there a subgroup of dual depth 3?

This post is motivated by an exchange with Zhengwei Liu. It is more than the dual version of this post, because we consider any subgroup (instead of just maximal), and even more at the end...
Let's ...

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### Is there a maximal subgroup of depth 3?

Let's first define what we mean by depth of a subgroup.
Let $G$ be a finite group and $H$ a subgroup. Let $(V_i)_{i \in I}$ and $(W_j)_{j \in J}$ be the irreducible complex representations of $G$ ...

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### Database subgroups of free group

Is there some database that contains "all" low-index normal subgroups of the free group on two generators?
Extension: does there exist such a GAP-database?
Thank you!

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### GAP/HAPcocyclic: How to work with CcGroups

This is probably not a conceptual question- but I would appreciate any suggestions.
I am trying to construct central extensions of certain infinite groups (for example, a crystallographic space ...

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### Interpreting $H^n(BG,\mathbb Z)$ when $G$ is an infinite discrete group

Suppose $G$ is a two-dimensional space group, for example a semidirect product of $\mathbb Z^2$ with a crystallographic point group such as $\mathbb Z_2$, where the action of $\mathbb Z_2$ on $\mathbb ...

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### Lie Algebra Module Decomposition in GAP

Let $\mathfrak{g}$ be a complex finite-dimensional Lie algebra and let $V$ be a finite-dimensional $\mathfrak{g}$-module. Is there a way for me to check in GAP or some other software package whether $...