Primitive permutation groups with a regular subgroup
Copyright policy )Primitive permutation groups with a regular subgroup
In the present paper all triples \((G,\Omega,X)\) are determined where \(G\) is a primitive permutation group acting on a finite set \(\Omega\) and containing a regular subgroup \(X\) in the case that the socle \(\text{soc}(G)\) of \(G\) is alternating, sporadic or an exceptional group of Lie type. Many further examples \((G,\Omega,X)\) are constructed with \(G\) a classical group. The case \(\text{soc}(G)=\text{P}\Omega_8^+(q)\) is also determined completely. In addition, the consequences of the results for Burnside-groups are discussed.
- Freie Universität Berlin Germany
Primitive permutation group, Orthogonal group, Simple group, Burnside-group, Permutation representation, classical groups, regular subgroups, factorizations, B-group, Characterization theorems for permutation groups, Linear algebraic groups over finite fields, sporadic groups, Simple groups: alternating groups and groups of Lie type, Factorization, alternating groups, Sporadic group, Burnside-groups, Algebra and Number Theory, socles, Almost simple group, finite primitive permutation groups, almost simple groups, Primitive groups, Classical group, orthogonal groups, Regular subgroup, B-groups, Permutation group
Primitive permutation group, Orthogonal group, Simple group, Burnside-group, Permutation representation, classical groups, regular subgroups, factorizations, B-group, Characterization theorems for permutation groups, Linear algebraic groups over finite fields, sporadic groups, Simple groups: alternating groups and groups of Lie type, Factorization, alternating groups, Sporadic group, Burnside-groups, Algebra and Number Theory, socles, Almost simple group, finite primitive permutation groups, almost simple groups, Primitive groups, Classical group, orthogonal groups, Regular subgroup, B-groups, Permutation group
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