Quasinormal subgroups of order p
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Authors: | John Cossey Stewart Stonehewer Giovanni Zacher |
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Institution: | (1) Australian National University, Canberra, ACT, 0200, Australia;(2) University of Warwick, Coventry, CV4 7AL, UK;(3) Università degli Studi di Padova, 35131 Padova, Italy |
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Abstract: | 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.
S. Stonehewer is grateful to the Australian National University for financial support during the preparation of this paper. |
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Keywords: | Quasinormal subgroup Minimal subgroup p-Group |
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