Abelianization of some finite metacyclic 2-groups

Abstract

A group G is metacyclic if it contains a cyclic normal subgroup K such that G/K is also cyclic. Finite metacyclic groups can be presented with two generators and three defining relations. In this work, we determine the structures of the derived subgroup, abelianization and itsWhitehead's quadratic functor of some finite nonabelian metacyclic 2-groups based on their classification done by Beuerle in 2005. In addition, the nonabelin tensor product for some cyclicgroups is determined.