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Stabilizer Limits of Strongly Stable Triples

Let G be a finite group. We say that (G, H, α) is a strongly stable triple if H ≤ G, α ∈ Irr(H) and (αG)H is a multiple of α. In this paper, we study the quasi-primitivity, inductors, and stabilizer limits of strongly stable triples. We show that under certain conditions all stabilizer limits of a strongly stable triple have equal degrees, thus generalizing the corresponding theorem of character triples due to Isaacs.