Quasinormal subgroups of order p^2
The location of quasinormal subgroups in a group is not particularly well known. Maximal ones always have to be normal, but little has been proved about the minimal ones. In finite groups, the difficulties arise in the p-groups. Here we prove that, for every odd prime p, a quasinormal subgroup of order p 2 in a finite p-group G contains a quasinormal subgroup of G of order p.
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