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Automorphism Orbits and Element Orders in Finite Groups : Almost-Solubility and the Monster.
・ISBN 978-1-4704-6544-5 paper US$ 85.00
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| 著者・編者 | Bors, Alexander / Giudici, Michael / Praeger, Cheryl E., |
|---|---|
| シリーズ | Memoirs of the American Mathematical Society |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2023 |
| ページ数 | 95 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-15810＞ |
解説
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.