# 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.

26
questions

**4**

votes

**1**answer

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### 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 $K_0(\mbox{mod-}A)$?
...

**2**

votes

**0**answers

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
$G$...

**1**

vote

**0**answers

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 ...

**0**

votes

**0**answers

58 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 $G$?

**4**

votes

**2**answers

164 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
...

**2**

votes

**2**answers

144 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 ...

**5**

votes

**2**answers

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 ...

**4**

votes

**0**answers

101 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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**0**answers

130 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(...

**2**

votes

**0**answers

53 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 ...

**2**

votes

**0**answers

51 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 ...

**5**

votes

**1**answer

131 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 ...

**6**

votes

**3**answers

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 $G$ ...

**4**

votes

**1**answer

183 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!

**1**

vote

**0**answers

54 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 ...