All Questions
Tagged with computational-group-theory computability-theory
7 questions
26
votes
2
answers
1k
views
Is the cohomology ring of a finite group computable?
Is there an algorithm which halts on all inputs that takes as input a finite group ($p$-group if you like) and outputs a finite presentation of the cohomology ring (with trivial coefficients $\mathbb{...
- 3,230
17
votes
0
answers
969
views
Groups generated by 3 involutions
Let $r(m)$ denote the residue class $r+m\mathbb{Z}$, where $0 \leq r < m$.
Given disjoint residue classes $r_1(m_1)$ and $r_2(m_2)$, let the class transposition
$\tau_{r_1(m_1),r_2(m_2)}$ be the ...
- 19.6k
8
votes
1
answer
338
views
How bad can the recursive properties of finitely presented groups be?
Any finitely presented group naturally gives rise to an edge-labeled graph (the Cayley graph) and I am considering paths through this graph. Paths correspond to infinite sequences of generators, so ...
- 258
6
votes
3
answers
872
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An element $g$ in a group such that neither $g=1$ nor $g\ne 1$ can be proved.
Edited (this question contains two versions of a similar question)
Is there some finitely presented group $G$ generated by $g_1,...,g_n$ such that
there is an element $g\in G$ expressed as a finite ...
- 14.3k
4
votes
2
answers
544
views
Membership problem in monoids
What is the simplest example of a monoid with undecidable membership problem? In other words, I'm looking for a concrete monoid $S$ such that there is no algorithm which takes elements $s_1,...,s_n$ ...
- 41
4
votes
1
answer
266
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Are (group theoretic) Markov properties on groups with decidable word problems, decidable?
(Link to SE duplicate: https://math.stackexchange.com/questions/4959071/are-group-theoretic-markov-properties-on-groups-with-decidable-word-problems)
The Adian-Rabin theorem says that if a property of ...
- 191
0
votes
0
answers
106
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A decision problem of an inverse problem in finite group theory
A finite group $G$ is called integral if there is a finite group $H$ such that $G\cong H'$.
In Araujo, Cameron, Casolo, Matucci's paper, integrals of groups, they tried to solve a problem as following:...
