On integral representations of finite groups and rings generated by character values

Abstract

We study realization fields and integrality of characters of finite subgroups of [Formula: see text] and related lattices with a focus on the integrality of characters of finite groups [Formula: see text]. We are interested in the arithmetic aspects of the integral realizability of representations of finite groups, order generated by the character values, the number of minimal realization splitting fields, and in particular, consider the conditions of realizability in the terms of Hilbert symbols and quaternion algebras and some orders generated by character values over the rings of rational and algebraic integers.