Automorphism orbits and element orders in finite groups almost-solubility and the monster / Alexander Bors, Michael Giudici, Cheryl E. Praeger.
| Author/creator | Bors, Alexander |
| Other author | Giudici, Michael, 1976- |
| Other author | Praeger, Cheryl E., 1948- |
| Format | Electronic |
| Publication Info | Providence : American Mathematical Society, 2023. |
| Description | v, 96 pages : illustrations ; 26 cm. |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| Series | Memoirs of the American Mathematical Society, 0065-9266 ; Volume 287, Number 1427 (fifth of 6 numbers) |
| Abstract | "For a finite group G, we denote by [omega](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) :[equals] [omega](G) - o(G) and q(G) :[equals] [omega](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 [omega](G) [equals] o(G)). We show that the index [absolute value]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 characterization of the Fischer-Griess Monster group M"-- Provided by publisher. |
| Bibliography note | Includes bibliographical references (pages 93-96). |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2023031315 |
| ISBN | 9781470465445 (paperback) |
| ISBN | (pdf) |