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 https://www.gap-system.org/contact/

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, archives of which are available 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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Which resources are available to self-study GAP?

Background: This year I'll do another Group Theory course ( Open University M336 ). In the past I have used Mathematica's AbstractAlgebra package but (although visually appealing ) this is no longer sufficient (i.e. listing subgroups of $S_4$ takes…
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Embedding as a subgroup

Suppose I am given two finite groups $G$ and $H$ (not too large: let's say their orders are around $10000$ and $100$ respectively, and the order of $H$ divides the order of $G$). These may be represented as groups of permutations with known, fairly…
Robert Israel
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Proof that the Rubik’s Cube group is 2-generated

Singmaster (1981) writes, on page 32 of his Notes on Rubik’s Magic Cube: Frank Barnes observes that the group of the cube is generated by two moves: \begin{align*} \alpha &= L^2 B R D^{-1} L^{-1} &=(RF,RU,RB,UB,LD,LB,LU,BD,DF,FL,RD)& \\ &&\cdot…
lynn
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How to solve this solvable 8th-degree algebraic equation by radicals?

Solve the following equation in radicals. $$x^8-8x^7+8x^6+40x^5-14x^4-232x^3+488x^2-568x+1=0$$ I use Magma to verify that its Galois group is a solvable group. R := RationalField(); R < x > := PolynomialRing(R); f :=…
D.Matthew
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Math-related open source software to contribute to

I'm interested in finding a math-related open source project that I can contribute to. I've studied maths and stats at undergraduate level, but I'm a professional software developer and I'll have some spare time in the next few months at least that…
TooTone
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How to find all subgroups of a group in GAP

With the next group: gap> G:=Group((1,2,3,4),(1,2)); Group([ (1,2,3,4), (1,2) ]) gap> Order(G); 24 gap> Elements(G); [ (), (3,4), (2,3), (2,3,4), (2,4,3), (2,4), (1,2), (1,2)(3,4), (1,2,3), (1,2,3,4), (1,2,4,3), (1,2,4), (1,3,2), (1,3,4,2), …
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The homophonic group: a mathematical diversion

By definition, English words have the same pronunciation if their phonetic spellings in the dictionary are the same. The homophonic group $H$ is generated by the letters of the alphabet, subject to the following relations: English words with the…
Miao
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Structure of the Brainball group

This is a Brainball: It consists of $13$ numbered pieces arranged in a ring and a core; each piece has one side white and one side yellow. Part of the core, the blue caps in the picture above, can flip two groups of $3$ and $4$ pieces at once like…
Parcly Taxel
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Cayley table group visualization

how can I make graphics like this? random colors. I got a script in GAP that prints rows of numbers but I want it colored just random colors G:=Units(Integers mod 2^3); n:=Order(G); M:=MultiplicationTable(G); for i in [1..n] do for j in [1..n]…
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Semidirect Products with GAP

I'm wondering how to specify to GAP which homomorphism to use when constructing a semidirect product. I'm trying to have it construct $\left(\mathbb{Z}_p\times\mathbb{Z}_p\right)\rtimes_\varphi S_3$. Since…
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Average number of strings with edit distance at most 4

Consider a binary string of length $n \geq 4$. An edit operation is a single bit insert, delete or substitution. The edit distance between two strings is the minimum number of edit operations needed to transform one string into the other one. …
user35671
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How to check in GAP whether two groups are isomorphic

Let $G,H$ be two Groups. How to check with GAP whether they are isomorphic or not? For example, GAP has IsNilpotentGroup to check whether the group $G$ is nilpotent. Is there a similar function named like AreIsomorphicGroups to check whether $G$ and…
A.G
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Modular subgroup lattice in GAP

I want to know if one can ask GAP to decide whether the subgroup lattice of a specific finite group $G$ is modular, via a simple command. Many thanks. Update: relevant questions have been addressed by Ballester-Bolinches, Cosme-Llópez, and…
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How is GAP generating all subgroups?

GAP can return all subgroups of $S_4$ pretty much instantaneously: gap> AllSubgroups(SymmetricGroup(4)); [ Group(()), Group([ (1,2)(3,4) ]), Group([ (1,3)(2,4) ]), Group([ (1,4)(2,3) ]), Group([ (3,4) ]), Group([ (2,3) ]), Group([ (2,4) ]),…
dharmatech
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Is this specific group finite?

I have the following group presentation: $G=\left\langle a,b,c\ |\ a^2,b^{11},c^2,(ab)^{4},(ab^2)^6,ab^2abab^{-1}abab^{-2}ab^2ab^{-1},(ac)^3,(bc)^2\right\rangle$ Is $G$ finite? GAP's Size(G) runs out of memory pretty quickly. No surprise there. I…
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