We say that $G$ is a homocyclic group, if it is direct product of isomorphic cyclic groups. Is there any classification of finite odd-order groups which all their Sylow subgroups are homocyclic?
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$\begingroup$ I am not aware of one. Do you think they would be substantially different from odd order groups with all Sylow subgroups Abelian? $\endgroup$– Geoff RobinsonMay 5, 2013 at 15:23
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$\begingroup$ I don't know, but a calssification of odd order groups with all Sylow subgroups abelian is also good. $\endgroup$– majid arezoomandMay 5, 2013 at 15:47
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