Regular orbits of symmetric and alternating groups

JOURNAL OF ALGEBRA

卷:458

Article

Fawcett, Joanna B.¹  O'Brien, E. A.²  Saxl, Jan³ 

[1] Univ Western Australia, Ctr Math Symmetry & Computat, Sch Math & Stat, 35 Stirling Highway, Crawley, WA 6009, Australia

[2] Univ Auckland, Dept Math, Private Bag 92019, Auckland, New Zealand

[3] Univ Cambridge, Ctr Math Sci, Dept Pure Math & Math Stat, Wilberforce Rd, Cambridge CB3 0WB, England

关键词: Regular orbits;    Symmetric group;    Alternating group;    Primitive groups;    Base size;   

DOI  :  10.1016/j.jalgebra.2016.02.018

来源: Elsevier

【 摘 要 】

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 classier the pairs (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 PG-module such that the order of F is prime and divides the order of G. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free