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.
NILPOTENT SUBGROUPS OF CLASS 2 IN FINITE GROUPS / Sabatini L.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - ELETTRONICO. - 150:(2022), pp. 3241-3244. [10.1090/proc/15933]
NILPOTENT SUBGROUPS OF CLASS 2 IN FINITE GROUPS
Sabatini L.
2022
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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