proposition: Lemma cyclicJ G x : cyclic (G :^ x) = cyclic G.
proof: Proof. apply/cyclicP/cyclicP=> [[y /(canRL (conjsgK x))] | [y ->]]. by rewrite -cycleJ; exists (y ^ x^-1). by exists (y ^ x); rewrite cycleJ. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice div) mathcomp(fintype bigop prime finset fingroup morphism) mathcomp(perm automorphism quotient gproduct ssralg) mathcomp(finalg zmodp poly)