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
820
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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 ...
- 6,100
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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 ...
0
votes
1
answer
76
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Computing whether two finite groups are isomorphic (in C++) [closed]
I need to algorithmically compute whether two given finite groups are isomorphic. Usually I only have generators of these groups.
The groups can get quite large as I'm working with subgroups of $S_{32}...
- 729
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votes
1
answer
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Character table for a covering group of $\mathbb{Z}_n \times \mathbb{Z}_m$
I’m considering the group $G = \mathbb{Z}_n \times \mathbb{Z}_m$ and its covering group
$$G^* = \langle \alpha, \beta, a|\alpha a = a\alpha, \beta a = a\beta, a^p = 1, \alpha^n = 1, \beta^m = 1, \...
- 1,065
5
votes
1
answer
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Character tables of Coxeter Groups
I'm interested in character tables of (irreducible) Coxeter groups. Certainly the character tables of the symmetric groups $ W(A_n) \cong S_{n+1} $ are easy to obtain, as are the dihedral groups.
But ...
- 8,542
1
vote
2
answers
75
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Counting orbits of permutation group acting on bit strings
Let $ G $ be a subgroup of $ S_n $. What is the the best way to count the number of orbits of $ G $ acting on the length $ n $ bit strings $ \mathbb{F}_2^n $?
Obviously permutations can only take a ...
- 8,542
2
votes
0
answers
77
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Multiplicity of irreducible characters inside symmetric powers of a faithful character
Let $ G $ be a finite group of order $ n $. Let $ f $ be a faithful representation of $ G $ and by abuse of notation let $ f $ also denote the corresponding character. It is my experience that for ...
- 8,542
2
votes
0
answers
84
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Automorphism group of $A_n$, $n \geq 7$ [duplicate]
I am trying to find the automorphism group of the alternating groups $A_n$. However, when it comes to $A_7$, I have found it difficult to prove that $\operatorname {Aut}(A_7) \cong S_7$. (I have ...
- 163
0
votes
0
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Restriction of Brauer characters in GAP
Let $p$ be a prime.
Let $G$ be a finite group and $H$ be a $p'$-subgroup of $G$.
Let $\varphi\in \mathrm{IBr}_p(G)$.
I would like to restrict $\varphi$ to $H$ by GAP.
My idea is to extend $\varphi$ to ...
- 521
2
votes
1
answer
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GAP orthogonal groups: Specifying the invariant bilinear form
If I read the GAP manual correctly, one should be able to specify the underlying invariant bilinear form, when constructing an orthogonal group. However, when I try something like:
...
- 83
3
votes
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answers
50
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Burnside groups with GAP system [closed]
My question is related to Burnside groups $B(n, 3)$ in the GAP system. I'm interested in ways to represent Burnside groups $B(n, 3)$ in GAP.
The obvious representation using relations (see example for ...
- 149
0
votes
0
answers
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Factoring out the socle of the projective-injectives for a quiver algebra
Let $A$ be a quiver given in the GAP-package QPA (https://folk.ntnu.no/oyvinso/QPA/) .
Question: Is there a fast/easy way to obtain $A/soc(U)$ (using QPA), where $U$ is the direct sum of all ...
- 2,332
1
vote
1
answer
46
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Ordering of group elements in MultiplicationTable vs CosetTable in GAP
I construct a finitely presented discrete group $G$ in GAP, a normal subgroup $H\triangleleft G$ of finite index $N$, and the factor group $G/H$ of order $N$. Assume for simplicity that $G$ has two ...
- 109
1
vote
0
answers
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Checking if matrices in $ SU(2) $ generate an $ S $-arithmetic group
I am reading Super-Golden-Gates for $PU(2)$ by Ori Parzanchevski and Peter Sarnak. If I understand correctly then in section 4.1.3 they seem to be saying that the matrices
$$
F:= \frac{1}{\sqrt{2}} \...
- 8,542
0
votes
1
answer
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how to calculate the automorphisms of a group that fix a subgroup
I have a finite (polycyclic) group $G$ and a subgroup $H<G$.
How do I calculate the subgroup of $Aut(G)$ that fixes $H$ pointwise : $S = \{ a \in Aut(G) : \forall h \in H,a(h)=h\}$
It would be nice ...
- 1,010