Nicky Hekster
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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