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G. Cutolo, H. Smith and J. Wiegold
On finite p-groups with subgroups of breadth 1
Bull. Aus. Math. Soc., 82, (2010), pp. 84–98.
doi: 10.1017/S0004972710000055
MathSciNet Zentralblatt Comments Abstract Full Text
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.
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