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bio website ms.uky.edu/~jack
location Lexington, KY
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visits member for 4 years
seen Aug 7 at 13:42

Aug
2
awarded  Yearling
Jul
31
revised Automorphisms of non-abelian groups of order 27
expand refs
Jul
12
awarded  Revival
Jul
8
answered Proving the Thompson Transfer Lemma
Jul
8
comment Proving the Thompson Transfer Lemma
@Nishant: use the representation on the cosets of M (rather than the left regular representation). More or less the same statements are true. I don't think you actually use transfer at all.
Jul
3
comment Question about inverse Galois problem
In 2, why aren't finite quotients of $\Lambda$ allowed as continuous quotients? For instance, why not the perfect group of order 120, $\operatorname{SL}(2,5)$?
Jul
2
answered A group of order $56$ with a unique Sylow $2$-group is either nilpotent or its Sylow $2$-group is $\cong (\mathbb{Z}/2 \mathbb{Z})^3$
Jul
2
comment A group of order $56$ with a unique Sylow $2$-group is either nilpotent or its Sylow $2$-group is $\cong (\mathbb{Z}/2 \mathbb{Z})^3$
What is your question? It seems like you see how the hint proves the proposition. Are you asking how to prove the hint (how to prove the action must be trivial or transitive)?
Jul
2
awarded  Socratic
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
30
comment Normally embedded subgroups reducing in a Hall system
@James: pretty literally that $G_\pi U$ is a subgroup. It means $G_\pi U = U G_\pi$; it is read “$G_\pi$ and $U$ permute.”
Jun
29
revised Is a finite group always a element-wise product of Sylow subgroups?
added 1247 characters in body
Jun
29
answered Is a finite group always a element-wise product of Sylow subgroups?
Jun
29
comment Is a finite group always a element-wise product of Sylow subgroups?
Finite solvable groups are characterized by the property that one can choose the $P_i$ such that $P_i P_j$ are subgroups. Finite nilpotent groups by the property that $[P_i,P_j]=1$.
Jun
27
comment Prove that if $H$ is a characteristic subgroup of $K$, and $K$ is a normal subgroup of $G$, then $H$ is a normal subgroup of $G$
This is a FAQ. math.stackexchange.com/questions/647058 math.stackexchange.com/questions/800164
Jun
26
comment Hopefully easy Lang-Steinberg computation: for Weyl elements
Looks good, I'm just writing up the translation.
Jun
26
comment Hopefully easy Lang-Steinberg computation: for Weyl elements
Thanks! I'll need to check everything for SL2 and then see if it works in general (though I think you are right, it should). This is fine for "not depending on q" (A single $\epsilon$ for each $q$ should work for all the $w_i$ in all the groups, so that is not too bad :-).
Jun
26
comment Hopefully easy Lang-Steinberg computation: for Weyl elements
@JyrkiLahtonen: yes
Jun
26
asked Hopefully easy Lang-Steinberg computation: for Weyl elements