Classification of finite p-groups with self-centralizing cyclic normal subgroup

From Groupprops
Jump to: navigation, search
This article gives a classification statement for certain kinds of groups of prime power order, subject to additional constraints.
View other such statements

Statement

A finite p-group (a group of prime power order) P, with a self-centralizing cyclic normal subgroup H, could be either of the following:

  • If p is an odd prime, it is a faithful semidirect product of cyclic p-groups: it is the semidirect product of H with a cyclic subgroup of the automorphism group of H.
  • If p = 2, there are a number of possibilities: PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

Related facts