On Finite Groups in Which Cyclic Subgroups of the Same Order are Conjugate |
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| Authors: | Mauro Costantini Enrico Jabara |
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| Affiliation: | 1. Dipartimento di Matematica Pura ed Applicata , Università di Padova , Padova, Italy costantini@math.unipd.it;3. Dipartimento di Matematica Applicata , Università di Ca' Foscari , Venezia, Italy |
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| Abstract: | 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, p m ), with m odd if p is odd, or to Sz(22m+1), or to one of the sporadic groups M 11, M 23, or J 1. |
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| Keywords: | Conjugacy classes Cyclic subgroups |
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