Nilpotent subgroups of class 2 in finite groups

Sabatini, Luca

doi:10.1090/proc/15933

Nilpotent subgroups of class $2$ in finite groups
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Proc. Amer. Math. Soc. 150 (2022), 3241-3244 Request permission

Abstract:

We show that every finite group $G$ of size at least $3$ has a nilpotent subgroup of class at most $2$ and size at least $|G|^{1/32\log \log |G|}$. This answers a question of Pyber, and is essentially best possible.

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