# 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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### How to check whether a finite $p$-group is regular in GAP?

I am trying to check whether a given $p$-group is a regular $p$-group in GAP. I am trying to use the command 'IsRegularPGroup(G)' for it. However I am getting 'Error, Variable: 'IsRegularPGroup' must ...
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### To find exponent of $1+J(F_2G)$ in GAP. [closed]

Please provide code in GAP to find the exponent of the normal subgroup $1+J(F_2G)$ of the unit group $U(FG)$ of the group algebra $FG$. Here $J$ stand for the Jacobson radical. Write the expression by ...
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1 vote
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### IsGroupOfAutomorphisms functionality

I'm looking for two things related to the GAP function IsGroupOfAutomorphisms: whether it does what I think it does (based on the brief GAP manual entry), and if so, how it works. The GAP manual ...
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### Automorphisms of a character table

Consider the character table of the finite group $G$. Every outer automorphism of $G$ permutes the characters of $G$. If some of the characters are non-integral then we can consider the ...
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### Distinct characters with the same character values, outer automorphisms and Galois conjugation

Given an (irreducible complex) character of a finite group the following three construction all yield another irreducible character of the same degree: multiplying by a degree 1 character applying an ...
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### Finding orbits of an action on a set of basis vector with GAP

I work with the computer algebra system GAP in this question. Let $K$ be a field (for example the rational numbers). I have a set $W$ consisting of sets of vectors basis of $K^n$ that only have ...
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### Intersection of Ideal in Gap(QPA)

I'm New to Gap(QPA). I'm trying to intersect Ideal in Gap and find their generators. For example here I construct some trivially intersecting ideals, Q:= Quiver(1,[[1,1,"a"],[1,1,"b&...
1 vote
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### Create matrix from permutations

I have a set of four permutations $\{(\cdots),(3,4),(2,4),(2,3)\}$. I want to create a $4 \times 4$ matrix with rows as above permutations. For example in this case matrix will be \begin{bmatrix} 1 &...
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### How often is a tensor product of two irreps of a finite group still irreducible?

All representations are considered over the complex numbers. Let $G$ be a finite group. Then Any 1-dimensional character $\otimes$ irreducible character is irreducible . But what if we have two ...
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### Comparing $GL(2,3)$ and the binary octahedral group

$\mathrm{GL}(2,3)$ is the group of $2 \times 2$ matrices over the field with 3 elements. It has $48$ elements and it is the Schur cover of $S_4$ of $+$ type, fitting into a central extension ...
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### Estimate the subgroup order of group of units in finite algebra in GAP

Let $G$ be a finite group $p$-group and $FG$ be a modular group algebra of $G$. Is there any way to estimate the order of subgroup generated by two or more elements of $U(FG)$, where $U(FG)$ is the ...
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### Counting groups based on PSU(4,3)

How many almost quasisimple extensions of PSU(4,3) are there? As noted in Constructing central extensions or Schur cover of U4(3) in GAP this group is too large to be in the perfect groups library (...
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1 vote
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### N-dimensional linear representation of symmetric group S(N)

A beginner's question on the linear representations of the symmetric group $S(n)$: playing around with GAP, e.g.: gap> CharacterDegrees(SymmetricGroup(n)); for ...
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### Is the affine special linear group perfect?

The special linear group $SL(n,q)$ is perfect, in fact quasisimple, for all $n \geq 2$ and $q$ prime power with the exception of $SL(2,2) \cong S_3$ and $SL(2,3)\cong 2.A_4$. Is it the case ...
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1 vote
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### Viewing monoid rings as rings with identity in GAP

I look at monoid algebra of finite monoids with GAP and want to force GAP to view them as algebras with one. But it seems it does not work: ...
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### All groups of order $112$ have an element of order $14$ [closed]

In finite groups there exists a very important class as Frobenius groups. We know that there exists a Frobenius group as $2^3:7$ which has an elementary abelian $2$-group. By the Properties of ...
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### Choosing Particular representation and/or identifying the representation of the group in GAP [closed]

I have three questions regarding the usage of GAP: I want to choose a particular matrix representation of a group, and thanks to the previous answer, I can display which representations are available,...
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### How to identify a group as a primitive group?

I have a problem identifying a group as a primitive group by using the function PrimitiveIdentification. Here is my code. ...
• 521
1 vote
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### Does every perfect finite group have a fixed point free representation?

Fixed point free representations of finite group are important for the spherical space form problem and also show up in other contexts for example Perfect semi direct products A representation $\pi$ ...
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### Writing the group over cyclotomic fields in GAP [duplicate]

I am able to define the group and do something with this group in GAP. For example, I am interested in the 2I group, and I can write this group in GAP simply as follows: ...
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### Is it possible to write a code that computes all the subgroups (up to isomorphism) of a finite Abelian group?

I am new to computational group theory. I am trying to find/write a program that computes the following: Input: a finite abelian group G \cong \mathbb{Z}_{m_1} \oplus \cdots \oplus \mathbb{Z}_{m_{...
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### How to make characteristics zero in GAP?

I have the following code written in GAP. In summary, In this code, I have a subgroup defined as SL(2,5). I applied the tensor product to each of these group elements with the identity and added a new ...
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1 vote
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### Canonical representation for sets in a group.

Let $G$ be a permutation group acting on a set $X$ of elements. Is there a known group theory operation "$\mathrm{Canon}$" such that, for each pair $A, B \subseteq X$ of elements subsets, \$\...
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