Upper bounds on derived length of Sylow subgroups related to irreducible character degrees in a finite group, indicating structural implications.
Let be a finite group and be a prime. We establish an upper bound for the derived length of a Sylow ‐subgroup of in terms of the number of irreducible characters of whose degrees are divisible by . We also prove that if is a ‐block of a finite ‐solvable group with defect group , then the derived length of is at most one more than the number of ordinary irreducible characters of positive height in .
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Cossey et al. (2026) studied this question.
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