Elements with similar properties usually deserve a name in many contexts, say primitive elements in finite fields, integers modulo a number $n$, generators of a free groups etc.

Does there exist a similar name for elements of a group generating the same cyclic subgroup?

  • $\begingroup$ Conjugate elements are similar, in the sense, on whatever set the group acts, the conjugate elements behave analogusly: if one element fixes some point, then so does its conjugate. On the other hand, the elements generating same cyclic subgroup (or conjugate cyclic subgroup) have special name rationally conjugate elements, which has origin in Representation Theory of groups. $\endgroup$ – Groups Nov 25 '15 at 6:02

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