A note on the monomial characters of a wreath product of groups

TL;DR

This paper investigates conditions under which the wreath product of a quasi-monomial or almost monomial group with a cyclic group of prime order retains these properties, expanding understanding of group character theory.

Contribution

It establishes that the wreath product preserves quasi-monomial and almost monomial properties under specific technical conditions.

Findings

Wreath product of a quasi-monomial group with a cyclic group is quasi-monomial under certain conditions.

Wreath product of an almost monomial group with a cyclic group is almost monomial under certain conditions.

Provides new insights into the structure of group characters in wreath products.

Abstract

Given a quasi-monomial, respectively an almost monomial, group $A$ and a cyclic group $C$ of prime order $p>0$, we show that the wreath product $W=A\wr C$ is quasi-monomial (respectively almost monomial), if certain technical conditions hold.