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- W2056426112 abstract "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 soc ( G ) ≅ P Ω 8 + ( q ) . In order to obtain all these triples, we also study the almost simple groups G with G ≅ P Ω 2 n + 1 ( q ) . The case G ≅ U n ( 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." @default.
- W2056426112 created "2016-06-24" @default.
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- W2056426112 date "2007-04-01" @default.
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- W2056426112 title "Primitive permutation groups with a regular subgroup" @default.
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- W2056426112 doi "https://doi.org/10.1016/j.jalgebra.2006.09.027" @default.
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