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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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        On monomial and $\Omega^d$-finite algebras

        Let $Q$ be a finite quiver and $I$ a monomial admissible ideal of the path algebra $KQ$ for a field $K$. Then an algebra $A=KQ/I$ is called a monomial algebra. It is well known that monomial algebras ...
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        1answer
        154 views

        Where or how can I find matrix representatives of the conjugacy classes of Conway's group Co??

        I would like to find ($24\times 24$) matrices representing the various conjugacy classes of Conway's group $\mathrm{Co}_0$ acting on the Leech lattice in the usual coordinate system given by the MOG. ...
        4
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        1answer
        116 views

        Testing whether a module generates $K_0(\mbox{mod-}A)$

        Given a representation-finite (connected) quiver algebra $A$ and a module $M$. Is there a good way to test whether the set $\{ [N] \mid N \in \mathrm{add}(M) \}$ generates $K_0(\mbox{mod-}A)$? ...
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        108 views

        About $E(G)$ for a finite $p$-group $G$

        For any group $G$, the absolute center $L(G)$ of $G$ is defined as $$L(G) = \lbrace g\in G\mid \alpha(g)=g,\forall\alpha\in Aut(G) \rbrace$$, where $Aut(G)$ denote the group of all automorphisms of $G$...
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        25 views

        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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        59 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
        167 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
        2answers
        148 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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        2answers
        147 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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        103 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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        132 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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        57 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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        votes
        0answers
        52 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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        1answer
        132 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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        3answers
        303 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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