Near integral domains on nonabelian groups

In this paper the concept of a special automorphism is introduced and used to analyze near integral domains having nonabelian addtive groups. We show that there are finite and infinite near integral domains having additive groups with arbitrary class of nilpotency. We also give another example of a non-nilpotent group which is the additive group of a near integral domain. Finally, nonabelian groups of order less than 1000 are examined to determine which can be the additive group of a near integral domain.Most of the results of this paper are contained in the author's doctoral dissertation at Boston University. The author thanks ProfessorD. W. Blackett for his guidance.