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Results tagged with gr.group-theory
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user 7108
Questions about the branch of algebra that deals with groups.
2
votes
1
answer
280
views
What finite simple groups appear as factors of surface fundamental groups?
Let $\Sigma_g$ be the a closed orientable surface of genus $g$.
My somewhat naive question: what is known about simple finite factors of $\pi_1(\Sigma_g)?$ In particular, I know that the composition …
- 7,952
8
votes
2
answers
1k
views
Is there a finitely presented group with infinite homology over $\mathbb{Q}$?
Suppose $G$ is a discrete group given by finitely many generators with finitely many relations. Can the homology groups $H_i(G, \mathbb{Q})$, or equivalently $H_i(BG, \mathbb{Q})$ (topological homolog …
- 7,952
4
votes
About Lie group $G$ has this escape property？
Let me rewrite a comment I made that has a typo, since it's too late to edit it. The property fails for any compact connected noncommutative Lie group. Note that if $G$ is a compact group then it has …
- 7,952
1
vote
Computationally intractable orbit of a monoid action on a finite set
Edit In my previous answer I took $M$ to be the set of elements with image $\{2,\dots, n\}$ together with a random involution. In fact, that answer does not produce a monoid, since the square of an in …
- 7,952