Paper «Real elements and p-nilpotence of finite groups» published in Adv. Group Theory Appl.

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Adolfo Ballester–Bolinches, Ramón Esteban-Romero, Luis Miguel Ezquerro Marín.
Real elements and p-nilpotence of finite groups.
Adv. Group Theory Appl., 2:25-30, 2016.

doi: 10.4399/97888548970143


Our first main result proves that every element of order 4 of a Sylow 2-subgroup S of a minimal non-2-nilpotent group G, is a real element of S. This allows to give a character-free proof of a theorem due to Isaacs and Navarro. As an application, the authors show a common extension of the p-nilpotence criteria proved by Berkovich and Isaacs and Navarro.

2020 Mathematics Subject Classification: 20D10, 20D20, 20D45.

Keywords: normal p-complement; control of fusion.