We show that every element of PSL(2, q) is a commutator of elements of coprime orders. This is proved by showing first that in PSL(2, q) any two involutions are conjugate by an element of odd order.
Pellegrini, M. A., Shumyatsky, P., Coprime commutators in PSL(2, q), <<ARCHIV DER MATHEMATIK>>, 2012; 99 (6): 501-507. [doi:10.1007/s00013-012-0465-0] [http://hdl.handle.net/10807/55567]
Coprime commutators in PSL(2, q)
Pellegrini, Marco Antonio;
2012
Abstract
We show that every element of PSL(2, q) is a commutator of elements of coprime orders. This is proved by showing first that in PSL(2, q) any two involutions are conjugate by an element of odd order.
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