Hypercyclic products of HCA-groups - Medenilla, Mark Anthony (Animo Repository, 2020)
A group G is said to be a Hall cyclic-by-abelian or an HCA-group if G con- tains a normal nilpotent subgroup N such that G/N0 is cyclic-by-abelian. It was also established that if G = HK where H and K are normal hypercyclic groups, then G is not necessarily hypercyclic. This paper determines suffi- cient conditions for H and K so that G = HK is hypercyclic and identifies classes of groups that would satisfy the given conditions: abelian groups, nilpotent groups, cyclic-by-abelian groups and HCA-groups. Some results about the product of finite HCA-groups are also given. Keywords: HCA-groups, hypercyclic groups, nilpotent groups, cyclic-by-abelian groups,