UNITARITY OF THE MULTIPLICATIVE GROUP OF AN INTEGRAL GROUP RING

Abstract

A homomorphism of a group into the multiplicative group of the ring of integers is called, in algebraic topology, an orientation homomorphism of the group .If is an element of the integral group ring , we will let denote the element . An element of the multiplicative group is called -unitary if the inverse coincides with or . The collection of all -unitary elements of the group form a subgroup . If , the group is said to be -unitary.Our study of the group is motivated by its appearance in algebraic topology, and was suggested by S. P. Novikov.The main result of this article consists of necessary conditions, given in terms of the kernel and an element such that , for the group to be -unitary. We also consider to what extent these conditions are sufficient.Bibliography: 3 titles.