Transitive Permutation Groups with Bounded Movement Having Maximal Degree

✍ Scribed by Akbar Hassani; Mehdi Khayaty; E.I Khukhro; Cheryl E Praeger

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 156 KB
• Volume: 214
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1998.7681

✦ Synopsis

Let G be a transitive permutation group on a set ⍀ such that G is not a 2-group and let m be a positive integer. It was shown by the fourth author that if < g < < < ? Ž . @ ⌫ _ ⌫ F m for every subset ⌫ of ⍀ and all g g G, then ⍀ F 2 mpr p y 1 , < < < < where p is the least odd prime dividing G . If p s 3 the upper bound for ⍀ is 3m, and the groups G attaining this bound were classified in the work of Gardiner, Mann, and the fourth author. Here we show that the groups G attaining the bound Ž . < < Ž .

* It was with great sadness that three of us learned of the death of our colleague Akbar Hassani of a heart attack on May 20, 1998, while this paper was being revised.