Counting in nilpotent injectors and Carter subgroups

TL;DR

This paper explores the number-theoretic properties of nilpotent injectors and projectors within finite soluble groups, focusing on their subgroup structures and related algebraic properties.

Contribution

It introduces new insights into the structure and properties of nilpotent injectors and projectors in finite soluble groups, expanding understanding of their algebraic behavior.

Findings

Characterization of nilpotent injectors in finite soluble groups

Identification of properties of nilpotent projectors containing specific subgroups

New results on the algebraic structure of these collections

Abstract

We investigate number-theoretic properties of the collection of nilpotent injectors or nilpotent projectors containing certain subgroups of finite soluble (or ${\mathcal N}$-constrained) groups.