# Questions tagged [gr.group-theory]

Questions about the branch of algebra that deals with groups.

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### A question about coprime automorphisms of profinite groups

Let $p$ a prime. A finite group is a $p'$-group if its order is prime to $p$. Let $A$ be a finite $p'$-group of automorphisms of a finite $p$-group $G$. Suppose that $A$ is a non-cyclic abelian group. ...
• 869
1 vote
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### Definition of free profinite product of infinitely many groups

If we have profinite groups $G_1,...,G_n$ we can define its free profinite product in the natural way. But this natural definition (similar to the abstract case but in the category of profinite groups)...
• 299
1 vote
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### Infinite closed subgroup of ${\rm SL}_{n}(\mathbb{F}_{p}[[T]])$ with full residual image

Let $\mathbb{F}_{p}$ be a finite field of order $p$, $\mathbb{Z}_p$ be the ring of $p$-adic integers and $\mathbb{F}_{p}[[T]]$ be the ring of formal power series over $\mathbb{F}_{p}$. For $p\geq 5$, ...
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### Model-theoretic construction of Gromov boundaries on groups

For context, I'm only a second year undergraduate mathematician, so I won't know much. For third year, I'm hoping to do a research project. I met up with a professor who might be my supervisor today, ...
• 101
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### $M^3$ admits $Sol$ geometry if and only if $\pi_1M$ is virtually solvable but not virtually nilpotent?

Let $M$ be a closed, orientable, irreducible 3-manifold and having an infinite fundamental group. Is it true that $M$ admits $Sol$ geometry if and only if $\pi_1M$ is virtually solvable but not ...
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### Can we find background noise for every Følner sequence in a countable amenable group?

Let $G$ be a countable amenable group. We consider sequences $(z_g)_{g\in G}$ of complex numbers with $|z_g|=1$ for all $g\in G$. I will say $(z_g)_{g\in G}$ is background noise for a (left-)Følner ...
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1 vote
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• 515
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### How might someone with a background in group theory start research into topos theory?

The Question: How might an early career mathematician with a background of research in group theory start research into topos theory? I want links between the two areas, not career advice, though it ...
• 369
147 views

### Up to what order have finite groups been classified? [duplicate]

All finite simple groups have been classified, and the classification of finite groups is thought to be wild. So, up to what order have finite groups been classified? Wikipedia tells us that it is ...