# Character triples and Shoda pairs

## TL;DR

This paper introduces a new method for constructing Shoda pairs using character triples, applicable to a broad class of monomial groups, and discusses their algebraic structure with illustrative examples.

## Contribution

It presents a novel construction of Shoda pairs via character triples for large classes of monomial groups, expanding existing algebraic techniques.

## Key findings

- Construction of Shoda pairs for monomial groups
- Computation of primitive central idempotents
- Analysis of simple components of rational group algebra

## Abstract

In this paper, a construction of Shoda pairs using character triples is given for a large class of monomial groups including abelian-by-supersolvable and subnormally monomial groups. The computation of primitive central idempotents and the structure of simple components of the rational group algebra for groups in this class are also discussed. The theory is illustrated with examples.