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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.

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

This is the tag for questions related to the computational algebra system 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 written in the GAP language as well as large data libraries of algebraic objects. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more.

Suggestions on using the gap tag:

  • please use it for new questions which explicitly ask something about the GAP system. This will help other GAP users who are reading math.SE to discover your question;

  • please don't use it for retrospective tagging of answered or commented questions where the answers/comments use GAP but most likely same calculation could be performed with any general-purpose computer algebra system;

  • in other cases, please use it with certain discretion, dependently on the potential learning value of the content of the discussion for other GAP users.

If you want to ask a question in this category, please note that there are well-established support channels for GAP users such as GAP Forum and GAP Support which may be more suitable places for such questions with a different (though possibly intersecting) audience, and with a different response rate (which may be faster or slower, dependently on your question). While there are certainly GAP users and some authors of GAP and/or its packages among the users of this Q&A site, please do not assume that the question on GAP asked here will necessarily be seen by the majority of GAP developers and package authors. On the other hand, research questions which may be of interest to wide ranks of GAP users are certainly welcomed here as well.

It may also happen that your question is already answered in the Frequently Asked Questions section of the GAP website or in the GAP Forum (to search GAP Forum archives, click here).

Finally, if you think that you have discovered a bug in the GAP system, the recommended way to report it is to use the GAP issue tracker on GitHub. Many packages have their own issue trackers, which you can find following the links here.

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How to rename variables in GAP during the whole program?

I'd like to ask the following question. I would like to write a GAP program which does the following in general what I will now only illustrate with an example. I have entered two quiver algebras modulo some relations in GAP, say $A_1=kQ_1/I_1$ and…
Bernhard Boehmler
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Error while calculating automorphism of non abelian group on Gap

I am implementing the following code to calculate the automorphism of non-abelian group on Gap. f := FreeGroup("b", "c"); # define free group f in two generators b := f.1; c := f.2; # call b and c the generators of f rels := [b^4,…
Ashish
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How to define the classical Lie algebras using the GAP package?

How to define using the GAP package, with the Lie algebra package included, some classical Lie algebras like sl(n,C), so(n,R), su(n) etc. without using commands referring to the type A_n? Possibly one has first to define the corresponding…
Jo Wehler
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Betti number and torsion coefficient

Is there any function in GAP to calculate Betti number and torsion coefficient of a group given? Thanks.
Angel Blasco
  • 536
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Listing elements which satisfy a property

A subgroup $H$ of $G$ is said to be pronormal in $G$ if for each $g \in G$, there exists $x\in \langle H, H^g \rangle$ such that $H^x = H^g$. A test for pronormality of a subgroup is given by the following GAP code: IsPronormal := function(G,H) …
R Maharaj
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Subgroup generated by two subgroups in GAP

I'm new to GAP and I'm not sure if MSE is the correct place to ask this. Let $G$ be a group with subgroups $H$ and $K$. How do I find input a command to find the subgroup generated by them both i.e. $\langle H, K \rangle$?
R Maharaj
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Equivalence classes in GAP

I have a list and a function on the elements on this list. I want to define an equivalence relation on this list by saying that two elements are equivalent if the function applied to those elements gives the same results. Is there a way to obtain…
Mare
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Finding subsets of a list in GAP

Is there a command in GAP to find all n-subsets of a list? So the input is a list and the output should be a list, which gives all n-subsets of the list in the input. Here an example of a list with 3 elements and wanting to find all sublists with 2…
Mare
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Problem with MappedWord

The setup I give here is only examplary but shows how I want to use MappedWord in diverse contexts. I have $S$ : A finite symmetric group with generators $s_1$ and $s_2$ $H$ : a known subgroup of $S$ generated by $h_1$ and $h_2$ $G$ : a group…
Marc Bogaerts
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Why does GAP takes this element as a generator?

I was trying to find an answer to my question. In fact I want to show that in the group $G = \{a,b | a^{2n},b^4,(ab)^2,(ab^-1)^2\}$ the elements $a$ and $b^2$ commute. Therefore I tried the following: F := FreeGroup("a",…
Marc Bogaerts
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Replace variable by value in gap

I want to generate a list of maps in a function and return this list. For example the list of maps $$ [k\mapsto k+1,\ k\mapsto k+2,\ k\mapsto k+3] $$ I thought I could do this by the following code: get_maps := function() local maps,i; maps…
Thorsten
  • 35
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Constructing the quasinilpotent residual with GAP

A (finite) quasinilpotent group $G$ is one that satisfies $\mathrm{F}^{\ast}(G)=G$, where $\mathrm{F}^{\ast}$ is the generalised Fitting subgroup of $G$. The class of quasinilpotent groups is a formation (cf. Huppert & Blackburn Finite Groups III…
the_fox
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Testing for Schmidt groups with GAP

I've written the following simple code to test (with GAP) whether a finite group $G$ is a Schmidt group, that is, a group which is not nilpotent but each of its proper subgroups is. IsSchmidtGroup := function(G) local M,i; i:=0;; if…
the_fox
  • 5,805
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Nilpotent matrix corresponding to a partition via gap

is there a command/quick way in GAP, that gives me the corresponding nilpotent Matrix in jordan normalform(as an element of the matrix algebra MatAlgebra(GF(a),b)) when I enter a Partition and a field? So ([2],GF(3)) should enter the matrix…
Mare
  • 2,332
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How to bypass breaking of loop in GAP

I was trying to find whether there exists a finite group with the following presentation: $$
Pritibhajan
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