On Finite Groups in Which Cyclic Subgroups of the Same Order are Conjugate.

We consider finite groups G for which any two cyclic subgroups of the same order are conjugate in G. We prove various structure results and, in particular, that any such group has at most one non-abelian composition factor, and this is isomorphic to PSL(2, pm), with m odd if p is odd, or to Sz(22m+1), or to one of the sporadic groups M11, M23, or J1. [ABSTRACT FROM AUTHOR]