Real Elements and Schur Indices of a Group

TL;DR

This paper investigates the relationship between real conjugacy classes and characters in finite groups, focusing on properties like strong reality and total orthogonality, and explores related questions and examples.

Contribution

It introduces a refined analysis of real elements and Schur indices in finite groups, emphasizing properties like strong reality and total orthogonality.

Findings

Raises new questions about real conjugacy classes and characters

Provides examples illustrating the refined properties studied

Explores the connection between group properties and character theory

Abstract

In this article we try to explore the relation between real conjugacy classes and real characters of finite groups at more refined level. This refinement is in terms of properties of groups such as strong reality and total orthogonality. In this connection we raise several questions and record several examples which have motivated those questions.