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On the Rarity of Quasinormal Subgroups

Cossey, Peter (John); Stonehewer, Stewart Edward


For each prime p and positive integer n, Berger and Gross have defined a finite p-group G = HX, where H is a core-free quasinormal subgroup of exponent pn-1 and X is a cyclic subgroup of order pn. These groups are universal in the sense that any other finite p-group, with a similar factorisation into subgroups with the same properties, embeds in G. In our search for quasinormal subgroups of finite p-groups, we have discovered that these groups G have remarkably few of them. Indeed when p is...[Show more]

CollectionsANU Research Publications
Date published: 2011
Type: Journal article
Source: Rendiconti del Seminario della Universita di Padova


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