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A nomadic postdoc, currently in Australia.

6h
comment quasiprimitive unsoluble groups
This paper is probably a good place to start: researchgate.net/publication/…
Jul
15
comment Products of subgroups that generate a finite group
There are also Zappa-Szep products, that is, groups of the form $AB$ for subgroups $A$ and $B$ such that $A \cap B$ is trivial. See for instance math.stackexchange.com/questions/107781/…
Jul
14
asked Separation of topological group elements by invariant neighbourhooods
Jul
13
answered Infimum of two group topologies
Jul
13
comment Reading Papers in a Language you don't Speak
Google Translate is a poor source of definitions for technical jargon, but Wikipedia is not bad. You should also make an effort to learn standard expressions, like "Soit... Alors..." and "genau dann, wenn...". Thankfully there are not many expressions to learn, as mathematical writing tends to be very 'stiff' and formulaic compared to ordinary prose.
Jul
12
comment Products of subgroups that generate a finite group
We have $|H_1H_2| = |H_1||H_2|/|H_1 \cap H_2|$, so you can determine whether $G = H_1H_2$ just by looking at orders of subgroups. Also, knowing how many steps it takes to cover the commutator group $[H_1,H_2]$ will give a good estimate, since $G = [H_1,H_2]H_1H_2$.
Jul
12
revised Locally compact vs. compactly generated in group theory
Answered original question
Jul
7
asked The set of (property) elements of a locally compact group is closed
Jul
7
answered What are the best settings for the large scale geometry of locally compact groups?
Jul
2
awarded  Inquisitive
Jul
2
awarded  Curious
Jun
17
awarded  Self-Learner
Jun
15
comment Classic applications of Baire category theorem
The Baire category theorem is very useful in topological group theory, because a subgroup either is open or has empty interior, and because there are still plenty of interesting open problems about topological groups that are locally compact and/or Polish.
May
28
comment Are norms intrinsically $\mathbb{R}$-valued?
I think what makes $\mathbb{R}$ special is that it is the largest Archimedean ordered group, so it naturally turns up in any sort of Archimedean norm.
May
14
comment Interesting examples of generic behavior of mathematical objects being either unreasonably structured or simply unreasonable
Not sure if this counts as an example: if you take a random $k$-element subset of the free profinite group $F$ on $d \ge 2$ generators, it will almost always be contained in a proper closed subgroup of $F$, for any $k$. What's interesting is that this is not the case, for instance, for the free prosoluble group on $d$ generators (provided $k$ is large enough).
May
13
answered Locally compact vs. compactly generated in group theory
May
13
comment Unconventional types of induction
Gerry Myerson: If your base case was instead to prove P(n) for infinitely many n (in a way that does not actually specify which n, e.g. 'by compactness, there is a subsequence on which f(n) converges...'), that ought to count as an unconventional induction.
Apr
29
comment Is there a precise notion of “almost all” such that almost all finite groups are Galois groups of extensions of the rationals?
Proving almost all finite groups are 2-groups looks hard, but perhaps it is reasonable to assert that almost all finite groups are soluble, since non-abelian simple groups are extremely sparse in the class of finite groups and don't admit many extensions.
Apr
28
comment Automorphisms of profinite groups
Yves Cornulier's comment answers the question for $n$ coprime to $p$: indeed, $\mathrm{Aut}(F)$ is pro-$p$-by-$\mathrm{GL}(d,p)$, so $F$ has an automorphism of order $n$ if and only if $n$ divides $|\mathrm{GL}(d,p)|$. The next question to ask is whether $F$ has automorphisms of order $p^k$ for arbitrarily large $k$.
Apr
27
revised Coprime automorphisms of finitely generated pro-$p$ groups
Added sufficient condition