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A nomadic postdoc, currently in Australia.
2d

revised 
Equations and random subgroups in compact groups
added 596 characters in body 
Aug 14 
asked  Equations and random subgroups in compact groups 
Aug 7 
comment 
A question on conjugacy classes of central involutions in a finite group
The question reduces to fusion in a Sylow $2$subgroup $S$ of $G$. We want to know, given $a \in S, b \in Z(S)$ distinct involutions that are in a given conjugacy class $C$ of $G$, does $ab$ lie in $C$? In other words, is $C'$ a union of cosets of $C' \cap Z(S)$, where $C' = (C \cup \{1\}) \cap S$? (We certainly need $C' \cap Z(S)$ to be a nontrivial group.) 
Aug 6 
comment 
A question on conjugacy classes of central involutions in a finite group
The condition is certainly necessary, since the product of two involutions is an involution if and only if they are distinct and commute. 
Aug 6 
revised 
Faithful representations of free prop groups
added 344 characters in body 
Aug 6 
answered  Faithful representations of free prop groups 
Jul 25 
comment 
Most Regularity of a Polygon
According to the Wikipedia article, the corners of the cube and dodecahedron do not give optimal configurations. So it's not just a matter of having the 'most regularity' in how they are arranged. 
Jul 25 
comment 
quasiprimitive nonsolvable groups
@PeterMueller: Ah yes. I was thrown by 'quasiprimitive group' and 'action' without any further qualification, which I have usually seen in the context of permutation groups, but the Manz and Wolf reference is indeed about quasiprimitive representations/characters. 
Jul 25 
comment 
quasiprimitive nonsolvable 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 ZappaSzep 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 $H_1H_2 = H_1H_2/H_1 \cap H_2$, 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  SelfLearner 