Finite p-groups in which every cyclic subgroup is 2-subnormal

Research Report MRR00-022

Finite p-groups in which every cyclic subgroup is 2-subnormal

Elizabeth A Ormerod

Abstract: This paper investigates finite p-groups, p \geq 5, in which every cyclic subgroup has defect at most two. This class of groups is often denoted by U_2,1. The main result is a theorem which characterises these groups by identifying a family of groups in U_2,1, and showing that any finite p-group in U_2,1, with p \geq 5, must be a homomorphic image of one of these groups.

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