Regular orbits of symmetric and alternating groups

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• 作者：Joanna B. Fawcett^a ; ^{joanna.fawcett@uwa.edu.au" class="auth_mail" title="E-mail the corresponding author} ; E.A. O'Brien^b ; ^{obrien@math.auckland.ac.nz" class="auth_mail" title="E-mail the corresponding author} ; Jan Saxl^c ; ^{j.saxl@dpmms.cam.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Regular orbits ; Symmetric group ; Alternating group ; Primitive groups ; Base size
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 July 2016
• 年：2016
• 卷：458
• 期：Complete
• 页码：21-52
• 全文大小：657 K

文摘

Given a finite group G and a faithful irreducible FG-module V where F has prime order, does G have a regular orbit on V  ? This problem is equivalent to determining which primitive permutation groups of affine type have a base of size 2. In this paper, we classify the pairs (G,V)$(G,V)$ for which G has a regular orbit on V where G is a covering group of a symmetric or alternating group and V is a faithful irreducible FG-module such that the order of F is prime and divides the order of G.