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comment Is every group of odd order isomorphic to a subgroup of $A_n$ for some $n$?
Actually $S_m$ embeds into $A_{m+2}$ but not in $A_{m+1}$, unless $m = 1$.
1d
comment Conjugacy classes of the nonabelian group of order 21
@RuianChen: Thanks, fixed.
1d
revised Conjugacy classes of the nonabelian group of order 21
edited body
Apr
22
awarded  Nice Answer
Apr
11
comment Given 3 distinct primes {$p,q,r$}, then $|G|=pqr \implies G$ not simple
So you get $\geq (p-1)q$ elements of order $p$, also $\geq (q-1)r$ elements of order $q$, and $\geq (r-1)pq$ elements of order $r$.. putting all this together gives you at least $pqr$ elements, and then you still have the identity
Mar
27
comment Question on proof that maximal normal abelian subgroup is self-centralising in nilpotent groups
$C_G(N)$ is normal if $N$ is normal. Furthermore in the proof $N$ is a central subgroup of $U$ and $U/N$ is cyclic, hence by (*) the subgroup $U$ must be abelian.
Mar
3
awarded  Disciplined
Mar
2
comment Non zero linear functional on X
What is $N(f)$?
Feb
18
awarded  Enlightened
Feb
18
awarded  Nice Answer
Feb
8
revised Can this lattice be realized as an intermediate subgroups lattice?
deleted 22 characters in body
Feb
8
comment Can this lattice be realized as an intermediate subgroups lattice?
@SébastienPalcoux: No idea, I only know about this result and have never looked at this paper in any detail. But see 8.1 and section 7 where $G$ is defined.
Feb
8
answered Can this lattice be realized as an intermediate subgroups lattice?
Feb
7
answered Relation between chief and compositions series of a group
Jan
31
awarded  Nice Answer
Jan
28
comment Finding the degree of $1+\sqrt[3]{2}+\sqrt[3]{4}$ over $\mathbb{Q}$
Yes, if you can elaborate on what is not clear.
Jan
2
comment Is $x \mapsto \text{Stabilizer}(x)$ an equivariant map?
The action on the conjugates of $H$ is conjugation, not left multiplication. So the claim is that $f(gx) = gf(x)g^{-1}$.
Dec
29
answered Characteristic subgroups of a direct product of groups
Dec
29
comment Maximal solvable subgroup not Borel
One example is the normalizer of a maximal torus in $\operatorname{SL}_2(\mathbb{C})$.
Dec
21
answered What does “exponent 2 nilpotency class 2” mean?