Abstract
Abstract Let p be a prime. We show that other than a few exceptions, alternating groups will have p-blocks with small defect for p equal to 2 or 3. Using this result, we prove that a finite group G has a normal Sylow p-subgroup P and G / P {G/P} is nilpotent if and only if φ ( 1 ) 2 {\varphi(1)^{2}} divides | G : ker ( φ ) | {|G:{\rm ker}(\varphi)|} for every irreducible Brauer character φ of G.
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