Seminormal and subnormal subgroup lattices for transitive permutation groups

• Autores: Cheryl E. Praeger
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 80, Nº 1, 2006, págs. 45-63
• Idioma: inglés
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• Resumen

  • Various lattices of subgroups of a finite transitive permutation group G can be used to define a set of `basic' permutation groups associated with G that are analogues of composition factors for abstract finite groups. In particular, G can be embedded in an iterated wreath product of a chain of its associated basic permutation groups. The basic permutation groups corresponding to the lattice L of all subgroups of G containing a given point stabiliser are a set of primitive permutation groups. We introduce two new subgroup lattices contained in L , called the seminormal subgroup lattice and the subnormal subgroup lattice. For these lattices the basic permutation groups are quasiprimitive and innately transitive groups, respectively.