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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? $\endgroup$ May 5, 2013 at 15:23
  • $\begingroup$ I don't know, but a calssification of odd order groups with all Sylow subgroups abelian is also good. $\endgroup$ May 5, 2013 at 15:47

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