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

Published online by Cambridge University Press:  26 February 2003

Elizabeth A. Ormerod
Elizabeth A. Ormerod
Affiliation:
Mathematics Department, Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia e-mail: Elizabeth.Ormerod@anu.edu.au
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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 {\cal U}_{2,1}. The main result is a theorem which characterises these groups by identifying a family of groups in {\cal U}_{2,1}, and showing that any finite p-group in {\cal U}_{2,1}, with p \geq 5, must be a homomorphic image of one of these groups.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 44 , Issue 3 , September 2002 , pp. 443 - 453
Copyright
2002 Glasgow Mathematical Journal Trust