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Sylow subgroups of transitive permutation groups II
| Content Provider | Scilit |
|---|---|
| Author | Praeger, Cheryl E. |
| Copyright Year | 1977 |
| Description | Let G be a transitive permutation group on a finite set of n points, and let P be a Sylow p-subgroup of G for some prime p dividing |G|. We are concerned with finding a bound for the number f of points of the set fixed by P. Of all the orbits of P of length greater than one, suppose that the ones of minimal length have length q, and suppose that there are k orbits of P of length q. We show that f ≦ $k_{p}$ − $i_{p}$(n), where $i_{p}$(n) is the integer satisfying 1 ≦ $i_{p}$(n) ≦ p and n + $i_{p}$(n) ≡ 0(mod p). This is a generalisation of a bound found by Marcel Herzog and the author, and this new bound is better whenever P has an orbit of length greater than the minimal length q. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2B245C4CD476238D8B7C105CF342A1B3/S1446788700018942a.pdf/div-class-title-sylow-subgroups-of-transitive-permutation-groups-ii-div.pdf |
| Ending Page | 332 |
| Page Count | 4 |
| Starting Page | 329 |
| ISSN | 14467887 |
| e-ISSN | 14468107 |
| DOI | 10.1017/s1446788700018942 |
| Journal | Journal of the Australian Mathematical Society |
| Issue Number | 3 |
| Volume Number | 23 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1977-05-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of the Australian Mathematical Society Permutation Group |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
