Talk «Carter and Gaschütz theories revisited» by María Dolores Pérez-Ramos at Ischia Online Group Theory Conference (GOThIC), 09/12/2021, 18.00

Dic ’21

The Organizing Committee of the  Ischia Online Group Theory Conference(GOThIC) is inviting you to a scheduled Zoom meeting.
– The TIME OF THE TALK is 18:00 CET (CET = UTC + 1). 
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– When joining, please  MAKE SURE THAT YOUR NICKNAME IS  YOUR NAME ANDSURNAME, or  close to it, so  that the organisers can recognise you and let you in.
TOPIC: GOThIC – Ischia Online Group Theory Conference –  (
TIME: Thursday December 9th, 2021 18:00 CET (UTC+1). 
COFFEE BREAK: The  talk will start at 18:00 CET.  The conference roomwill open at 17:45 CET for a drink – Bring Your Own appropriate drink – biscuits appreciated – and join us for some smalltalk before the event.
SPEAKER: Maria Dolores Pérez -Ramos (Universitat de València)
TITLE: Carter and Gaschütz theories revisited

ABSTRACT: Classical results from the theory of finite soluble groups state that Carter subgroups, i.e. self-normalizing nilpotent subgroups, coincide with nilpotent projectors and with nilpotent covering subgroups, and they form a non-empty conjugacy class of subgroups, in soluble groups. We present an extension of these facts to π-separable groups, for sets of primes π, by proving the existence of a conjugacy class of subgroups in π-separable groups, which specialize to Carter subgroups within the universe of soluble groups.

The approach runs parallel to the extension of Hall theory from soluble to π-separable groups by Cunihin, regarding existence and properties of Hall subgroups. Our Carter-like subgroups enable an extension of the existence and conjugacy of injectors associated to Fitting classes to π-separable groups, in the spirit of the role of Carter subgroups in the theory of soluble groups. This is joint work with M. Arroyo-Jordá, P. Arroyo-Jordá, R. Dark and A.D. Feldman.