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1d
answered meaning of a subgroup normalizes .
1d
answered $H$ is a subgroup of $G$ with finite index. Prove that G has finitely many subgroups of form $xHx^{-1}$
2d
answered Subgroup generated by a maximal subgroup and a conjugate of itself
May
3
comment Subgroup generated by a maximal subgroup and a conjugate of itself
If $\langle M, g^{-1}Mg \rangle = M$, then it follows that $g^{-1}Mg \subseteq M$, hence $M \subseteq gMg^{-1}$ and by the maximality of $M$ this gives $M=g^{-1}Mg$.
May
3
comment Subgroup generated by a maximal subgroup and a conjugate of itself
$M$ can be normal...
May
1
answered Quotient involving $\pi$-subgroups
Apr
29
comment about minimal non-nilpotent groups
Yes that is exactly what I mean. And being infinitely generated is important. Since a finitely generated subgroup must be proper, it is nilpotent. So the definition of AN groups is quite subtle.
Apr
29
comment about minimal non-nilpotent groups
Hmm, I am reading the paper now link.springer.com/article/10.1007%2FBF01589192#page-1 and they say that AN-groups are by definition not finitely generated. But you are right, since every proper subgroup is by definition nilpotent, it follows that AN-groups are locally nilpotent. This is important, since a lot is known about this class of groups. So that maybe the reason to note this explicitly.
Apr
29
comment about minimal non-nilpotent groups
Locally "something"means that every finitely generated subgroup has this property "something".
Apr
29
revised about minimal non-nilpotent groups
added 1 character in body
Apr
29
comment Automorphisms of infinite abelian groups
I found this relevant link: mathoverflow.net/questions/30572/…
Apr
27
comment Automorphisms of infinite abelian groups
Excellent Jeremy!
Apr
27
accepted Automorphisms of infinite abelian groups
Apr
25
revised Automorphisms of infinite abelian groups
added 12 characters in body
Apr
25
comment Automorphisms of infinite abelian groups
Yes I mean a non-trivial group of course. Will edit, thanks.
Apr
25
asked Automorphisms of infinite abelian groups
Apr
25
comment On normal $p$-complements
You are welcome!
Apr
23
answered Difference between conjugacy classes and subgroups?
Apr
23
revised Square of order of a Sylow p-subgroup in the nonabelian simple groups
edited tags
Apr
23
revised p-nilpotency and normality
added 573 characters in body