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

Alexander Bors, Michael Giudici, Cheryl E. Praeger

ISBN 10: 1470465442 / ISBN 13: 9781470465445

Published by American Mathematical Society, US, 2023

About this Item

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.

Seller Inventory # LU-9781470465445

Bibliographic Details

• Title: Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster
• Publisher: American Mathematical Society, US
• Publication Date: 2023
• Language: English
• ISBN 10: 1470465442
• ISBN 13: 9781470465445
• Binding: Paperback
• Condition: New