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- W2112020934 abstract "Let p be a fixed prime, G a finite group and P a Sylow p-subgroup of G. The main results of this paper are as follows: (1) If gcd (p-1, |G|) = 1 and p 2 does not divide |x G | for any p′-element x of prime power order, then G is a solvable p-nilpotent group and a Sylow p-subgroup of G/O p (G) is elementary abelian. (2) Suppose that G is p-solvable. If p p-1 does not divide |x G | for any element x of prime power order, then the p-length of G is at most one. (3) Suppose that G is p-solvable. If p p-1 does not divide χ(1) for any χ ∈ Irr (G), then both the p-length and p′-length of G are at most 2." @default.
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- W2112020934 date "2013-10-10" @default.
- W2112020934 modified "2023-10-17" @default.
- W2112020934 title "ON CONJUGACY CLASS SIZES AND CHARACTER DEGREES OF FINITE GROUPS" @default.
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- W2112020934 doi "https://doi.org/10.1142/s0219498813501004" @default.
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