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It has been shown by Cossey & Stonehewer (in the Padova Rendiconti 2011) that excessively large sections of finite p-groups can be devoid of quasinormal subgroups, bringing to an end the hope of relating group & subgroup-lattice structures via this concept. The present work begins the quest to find a generalisation of quasinormality that will be more successful.
DOI: 10.1017/S000497271100337
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