Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster - Couverture souple

Bors, Alexander; Giudici, Michael; Praeger, Cheryl E.

Couverture souple

ISBN 10 : 1470465442 ISBN 13 : 9781470465445

Editeur : American Mathematical Society, 2023

Synopsis

For a finite group G, we denote by ?(G) the number of Aut(G)-orbits on G, and by o(G) the number of distinct element orders in G. In this paper, we are primarily concerned with the two quantities d(G) := ?(G) ? o(G) and q(G) := ?(G)/ o(G), each of which may be viewed as a measure for how far G is from being an AT-group in the sense of Zhang (that is, a group with ?(G) = o(G)). We show that the index |G : Rad(G)| of the soluble radical Rad(G) of G can be bounded from above both by a function in d(G) and by a function in q(G) and o(Rad(G)). We also obtain a curious quantitative characterisation of the Fischer-Griess Monster group M.

A propos du livre

À propos de l?auteur

Alexander Bors, Carleton University, Ottawa, Canada, The University of Western Australia, Crawley, Australia, and Radon Institute for Computational and Applied Mathematics, Linz, Austria.

Michael Giudici, The University of Western Australia, Crawley, Australia.

Cheryl E. Praeger, The University of Western Australia, Crawley, Australia.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2023
• Langue: anglais
• ISBN 10: 1470465442
• ISBN 13: 9781470465445
• Reliure: Broché
• Nombre de pages: 95
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible