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In this paper, we consider lifts of π-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 such a lift. With this condition, we will get a lower bound on the number of such lifts.

Lifts of Partial Characters with Respect to a Chain of Normal Subgroups