threecyclegen. Fix three positive integers n, k, m Prove that a group subgroup H of S_{6+(n+k+m)} generated by g1:=G!(1,6,4,3,a_1,...a_n); g2:=G!(1,2,4,5,b_1,...,b_k); g3:=G!(5,6,2,3,c_1,...,c_m); H:=sub<G|[g1,g2,g3]>; satisfies H = S_{6+(n+k+m)} or H = A_{6+(n+k+m)}.

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