Isaacs' Generalization of Taketa's theorem

TL;DR

This paper extends the concepts of pseudo monomial characters and M-groups to Brauer and Isaacs' π-partial characters, proving a generalized Taketa's theorem and exploring related analogs in these settings.

Contribution

It introduces a generalized framework for pseudo monomial characters and M-groups within Brauer and Isaacs' π-partial character theories, including a new version of Taketa's theorem.

Findings

Proved an analog of Isaacs's generalization of Taketa's theorem in Brauer and π-partial settings.

Extended the concept of M-groups to new character frameworks.

Explored other analogs of M-group results in these generalized contexts.

Abstract

We generalize the definition of pseudo monomial characters and $M$-groups to the Brauer character and Isaacs' $\pi$-partial character settings. We prove an analogs of Isaacs's generalization of Taketa's theorem in those settings. We consider other analogs of results regarding $M$-groups in those settings.