Nilpotent subgroups of class $2$ in finite groups

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.

arXiv comment3 pages

References in corpus (1)

• Unsolved Problems in Group Theory. The Kourovka Notebook

Cited by in corpus (3)

• The growth of abelian sections
• On groups with large verbal quotients
• Probabilistic construction of some extremal $p$-groups