Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster
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A01=Alexander Bors
A01=Cheryl E. Praeger
A01=Michael Giudici
Author_Alexander Bors
Author_Cheryl E. Praeger
Author_Michael Giudici
Category=PBK
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eq_isMigrated=2
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Product details
- ISBN 9781470465445
- Dimensions: 178 x 254mm
- Publication Date: 31 Jul 2023
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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.
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.
Michael Giudici, The University of Western Australia, Crawley, Australia.
Cheryl E. Praeger, The University of Western Australia, Crawley, Australia.
