Automorphism Orbits and Element Orders in Finite Groups: Almost-Solubility and the Monster - Alexander Bors, Michael Giudici, Cheryl E. Praeger

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

Buch | Softcover
95 Seiten
2023
American Mathematical Society (Verlag)
978-1-4704-6544-5 (ISBN)
98,20 inkl. MwSt
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).
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.

Erscheinungsdatum
Reihe/Serie Memoirs of the American Mathematical Society ; Volume: 287 Number: 1427
Verlagsort Providence
Sprache englisch
Maße 178 x 254 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 1-4704-6544-2 / 1470465442
ISBN-13 978-1-4704-6544-5 / 9781470465445
Zustand Neuware
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