AgGroupOps.IsCyclic( G )
AgGroupOps.IsCyclic returns false if G is no abelian group.
Otherwise G is finite of order p_1^{e_1} ... p_n^{e_n} where the
p_i are distinct primes then G is cyclic if and only if each
<G>^{p_i} has index p_i in G.
AgGroupOps.IsCyclic computes the groups <G>^p_i using the fact that
the map x mapsto x^{p_i} is a homomorphism of G, so that the
p_i.th powers of an induced generating system of G are a homomorphic
image of an igs (see Cel92).
GAP 3.4.4