On transitive permutation groups with a subgroup satisfying a certain conjugacy condition

Journal of the Australian Mathematical Society

Cheryl E. Praeger¹ 

关键词: 20 B 05;    20 B 10;   

DOI  :  10.1017/S1446788700027348

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let G be transitive permutation group of degree n and let K be a nontrivial pronormal subgroup of G (that is, for all g in G, K and Kg are conjugate in (K, Kg)). It is shown that K can fix at most ½(n – 1) points. Moreover if K fixes exactly ½(n – 1) points then G is either An or Sn, or GL(d, 2) in its natural representation where n = 2d-1 ≥ 7. Connections with a result of Michael O'Nan are dicussed, and an application to the Sylow subgroups of a one point stabilizer is given.

【 授权许可】

Unknown