Centralizer-factorizable groups (Q790934)

A group G is said to be centralizer-factorizable if the centralizer of each subgroup of G is complemented in G. The author shows in this paper that nilpotent subgroups of a centralizer factorizable group are abelian. He then proves that a centralizer-factorizable group with an abelian commutator subgroup is decomposed into a semidirect product of two of its abelian subgroups satisfying certain conditions. Finally necessary and sufficient conditions for a finite group to be centralizer-factorizable are obtained.