# 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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### 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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### GAP Isomorphism between two finitely presented p-groups [closed]

I have finitely presented p-groups G and H of order 5^6 and i want to find isomorphism between them. I need to know image of generators [x1, x2, x3, x4] of group G. I tried using ...
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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,...
1 vote
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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. ...
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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1 vote
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### Irreducible representations of the symmetric group in GAP

I try to find the irreducible representation of the symmetric group (over the complex numbers) in a quick way using GAP. I made the following program that gives the irreducible representation ...
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### Computing power of element in GAP [duplicate]

I am trying to find powers of element in GAP; I defined a group G; When I print G, it shows Group( [ a1, a2, a3, a4, a5, a6 ] ); But if I compute a1^3; It shows "Error, Variable: 'a1' must have a ...
1 vote
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### Group action in GAP

I want to define a group action of group $G$ on set $X$, $G \times X \to X$ in GAP. I read the manual but I couldn't understand how. For example, I want to define group action of group $G$ on itself ...
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### Groups, Algorithms and Programming (GAP 4) lack of functions

I am a newbie in using of GAP. To learn it I downloaded a book "Groups, Algorithms and Programming" (subtitle GAP 3.4.4 of 20 Dec. 1995, gap3-jm of 19 Feb. 2018) and also Reference Manual of ...
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### Irreducible representation over finite field GAP

I have a finite group $G$ with $p\not \mid |G|$ and I want to compute an explicit modular representation of $G$ given a character $\chi$. I can compute a representation by ...
I have a finite group $G$ and an elementary abelian group $E(p^h)$ where $p\not \mid |G|$. I just want to construct via GAP the semidirect product $E(p^h):G$ given by a character $\chi$ of $G$, not ...
Let $A$ be a local(not necessarily commutative) finite dimensional algebra over a (finite if it helps) field $K$. Is there a way to check with GAP (without using QPA as we do not know quiver and ...