Research ArticleNo Access

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

Dipartimento di Matematica, Università degli Studi di Padova, “Tullio Levi-Civita”, Via Trieste 63, 35121 Padova, Italy

https://doi.org/10.1142/S0219498823501207Cited by:0 (Source: Crossref)

Abstract

We study realization fields and integrality of characters of finite subgroups of ${GL}_{n} (C)$ and related lattices with a focus on the integrality of characters of finite groups $G$ . 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.

Communicated by V. Futorny

Keywords:

AMSC: 20C15, 11R04

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