it was shown in [a. azimifard, e. samei, n. spronk, jfa 256 (2009)] that the zl-amenability constant of a finite group is always at least~$1$, with equality if and only if the group is abelian. it was also shown in [a. azimifard, e. samei, n. spronk, op cit.] that for any finite non-abelian group this invariant is at least $301/300$, but the proof relies crucially on a deep result of d. a. ride...

Abstract If p and q are primes, G is a -solvable finite group, it possible to detect that -Sylow normalizer contained in using the character table of . This characterized terms degrees -Brauer characters. Some consequences, which include yet another generalization Itô–Michler theorem, also obtained.