Archivo de la etiqueta: Control of fusion

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

Abstract:

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.

Paper “On the focal subgroup of a saturated fusion system” published in J. Algebra

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Adolfo Ballester-Bolinches, Luis M. Ezquerro, Ning Su, and Yanming Wang.

On the focal subgroup of a saturated fusion system.

J. Algebra, 468:72–79, 2016

https://doi.org/10.1016/j.jalgebra.2016.07.034

Abstract

The influence of the cyclic subgroups of order p or 4 of the focal subgroup of a saturated fusion system F over a p-group S is investigated in this paper. Some criteria for normality of S in F as well as necessary and sufficient conditions for nilpotency of F are given. The resistance of a p-group in which every cyclic subgroup of order p or 4 is normal, and earlier results about p-nilpotence of finite groups and nilpotency of saturated fusion systems are consequences of our study.

2010 Mathematical Subject Classification: 20C20

Keywords: Saturated fusion system, Control of fusion