Lifts of partial characters with respect to a chain of normal subgroups

TL;DR

This paper studies special lifts of partial characters in group theory, showing they can be induced from inductive pairs and providing bounds on their quantity.

Contribution

It introduces the concept of inductive pairs for lifts of partial characters and establishes their role in character induction and counting.

Findings

Lifts are induced from inductive pairs.

Every character from an inductive pair is a lift.

Provides a lower bound on the number of such lifts.

Abstract

In this paper, we consider lifts of $\pi$-partial characters with the property that the irreducible constituents of their restrictions to certain normal subgroups are also lifts. We will show that such a lift must be induced from what we call an inductive pair, and every character induced from an inductive pair is a such a lift. With this condition, we will get a lower bound on the number of such lifts.