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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.

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        45 views

        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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        2answers
        146 views

        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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        votes
        1answer
        103 views

        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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        votes
        2answers
        142 views

        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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        votes
        0answers
        93 views

        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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        123 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(...
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        votes
        0answers
        48 views

        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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        0answers
        48 views

        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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        votes
        1answer
        124 views

        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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        votes
        3answers
        300 views

        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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        votes
        1answer
        176 views

        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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        0answers
        50 views

        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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        votes
        0answers
        119 views

        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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        vote
        0answers
        68 views

        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 $...
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        0answers
        122 views

        Use GAP program to obtain explicit cocycles in group cohomology

        I'm trying to compute group cohomology $H^n(G,\mathbb{Z})$ of some crystal groups $G$ which are infinite but finitely generated groups. I succeed in obtaining cohomology groups using projective ...

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