Primitive permutation groups with a regular subgroup
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- 作者：Barbara Baumeister
- 关键词：Permutation group ; Primitive permutation group ; Regular subgroup ; Almost simple group ; Simple group ; Classical group ; Sporadic group ; Orthogonal group ; Factorization ; Permutation representation ; Burnside-group ; B-group
- 刊名：Journal of Algebra
- 出版年：2007
- 出版时间：15 April 2007
- 年：2007
- 卷：310
- 期：2
- 页码：569-618
- 全文大小：445 K
文摘
This paper starts the classification of the primitive permutation groups (G,Ω) such that G contains a regular subgroup X. We determine all the triples (G,Ω,X) with soc(G) an alternating, or a sporadic or an exceptional group of Lie type. Further, we construct all the examples (G,Ω,X) with G a classical group which are known to us. Our particular interest is in the 8-dimensional orthogonal groups of Witt index 4. We determine all the triples (G,Ω,X) with . In order to obtain all these triples, we also study the almost simple groups G with 13735ec354ecbfd2faf0e3a2c023"" title=""Click to view the MathML source"">GPΩ2n+1(q). The case GUn(q) is started in this paper and finished in [B. Baumeister, Primitive permutation groups of unitary type with a regular subgroup, Bull. Belg. Math. Soc. 112 (5) (2006) 657–673]. A group X is called a Burnside-group (or short a B-group) if each primitive permutation group which contains a regular subgroup isomorphic to X is necessarily 2-transitive. In the end of the paper we discuss B-groups.