We consider finite p-groups G in which every cyclic subgroup has at most p conjugates. We show that the derived subgroup of such a group has order at most p^2. Further, if the stronger condition holds that all subgroups have at most p conjugates then the central factor group has order p^4 at most.
On finite p-groups with subgroups of breadth 1 / Cutolo, Giovanni; H., Smith; J., Wiegold. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - STAMPA. - 82:(2010), pp. 84-98. [10.1017/S0004972710000055]
On finite p-groups with subgroups of breadth 1
CUTOLO, GIOVANNI;
2010
Abstract
We consider finite p-groups G in which every cyclic subgroup has at most p conjugates. We show that the derived subgroup of such a group has order at most p^2. Further, if the stronger condition holds that all subgroups have at most p conjugates then the central factor group has order p^4 at most.File in questo prodotto:
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