A Note on Supersoluble Groups

Johnson, D. L.

Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 562-564

Résumé

Let H be a subgroup of a group G (all groups considered throughout this article are finite); then H will be called primitive if the subgroup is distinct from H. Such subgroups, which are also called meet-irreducible, arise naturally in connection with minimal permutation representations of groups and in other contexts; for example, every subgroup of a group G can be written as an intersection of primitive subgroups of G, and the set of all primitive subgroups of G is characterized by its minimality with respect to this property. While maximal subgroups are always primitive, most groups contain non-maximal subgroups which are primitive (see remark at end of article). Note that a subgroup H of an abelian group G is primitive if, and only if, G/H is cyclic of prime-power order.

Détail

DOI : 10.4153/CJM-1971-063-5

Bibliographie

[1] 1. Huppert, B., Endliche Gruppen, Vol. I (Springer-Verlag, Berlin, 1967). Google Scholar