W. Burnside has proved that if a Sylow p-subgroup 𝑃 of a finite group 𝐺 is abelian and 𝑁𝐺(𝑃) = 𝐶𝐺(𝑃), then 𝑃 has a normal complement, that is 𝐺 is p-nilpotent. This result has been extended ...
If G is a finite group, p is a prime, and P is a Sylow p-subgroup of G, we study how the exponent of the abelian group P/P′ is affected and how it affects the values of the complex characters of G.
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