-2
votes
0answers
93 views

Given a set of generators of a group G, is there a method to find a presentation for G using those generators? [migrated]

Suppose I have a group $G$, which I know is finitely presentable and infinite. (In particular, I have a presentation for it, though not the one I want). Suppose I have a small list of generators ...
6
votes
1answer
276 views

Using math software to show that the following groups are infinite?

I would like to show that the following finitely presented group in 3 generators $P, Q, R$ is infinite in certain cases: $$P^p, Q^q, R^r, (PQ)^2, (QR)^2, (PQR)^2, (QR^{r/2+1})^a (RQR^{r/2})^b$$ For ...
2
votes
1answer
108 views

Finding particular reduced words for Weyl group elements

I am studying cluster algebra structures on the coordinate rings of partial flag varieties, as defined in the paper Partial flag varieties and preprojective algebras by Geiss, Leclerc and Schröer. One ...
1
vote
1answer
203 views

Sage or Magma Implementation of Nilpotent Orbit Varieties

For a given partition $[n_{1},...,n_{k}]$ of $N \in \mathbb{N}$ there exists a corresponding nilpotent orbit variety $O_{[n_{1},...,n_{k}]}$ in $\mathfrak{gl}(N)$ which can be represented by a set of ...
1
vote
2answers
184 views

My output of a group and inverse-closed subset in MAGMA is no longer inverse-closed when entered as input to GAP.

In MAGMA, I input the following: G:=SmallGroup(20,3); G; E:=[xx:xx in G]; S:=[E[6],E[7],E[13],E[20]]; S; S[1]^2; S[2]^2; S[3]*S[4]; This gives the output: GrpPC : ...
7
votes
4answers
917 views

Program for computing group cohomology

Is there any computer program with which I can compute the group cohomology H^n(G,V) for a group G acting linearly on a vector space? I mainly care about infinite groups.
1
vote
1answer
246 views

Homomorphisms and their restrictions in MAGMA

I am trying to look at a representation (so a homomorphism) of a group G, and see what the restriction of the representation to a subgroup of G will be. Is there an easy way (or any way!) to do this ...
2
votes
1answer
343 views

Finding Presentations of Groups with GAP

Group $A_5$ has presentation $〈 a, b | a^2 = b^3 = (ab)^5 = 1 〉$. Items equal to 1 are relators, so a presentation of $A_5$ as a set of relators could be $(a^2, b^3, (ab)^5)$ $Q_{16}$ is ...
5
votes
3answers
1k views

Using MAGMA for Group Theory

I've just started a PhD in Group Theory and need to use the computer programme MAGMA. I wonder if anyone could help me with a couple of (probably very basic things). I need to produce a Hasse ...
4
votes
1answer
154 views

Expressing a element of a Matrix subgroup in terms of subgroup generators

I'm no (computational) algebraist, and my searches have been pretty unyielding (probably due to the vast amounts written on the key words), but perhaps someone may know if this is possible, and if so, ...