Article ID Journal Published Year Pages File Type
4584484 Journal of Algebra 2015 21 Pages PDF
Abstract

Let G be a finite solvable group, let p   be a prime such that p≥5p≥5 and Op(G)=1Op(G)=1, and we denote |G|p=pn|G|p=pn, then G   contains a block of defect less than or equal to ⌊3n5⌋. Let G   be a finite solvable group and let papa be the largest power of p   dividing χ(1)χ(1) for an irreducible character χ of G  , we show that |G:F(G)|p≤p3a|G:F(G)|p≤p3a for p≥5p≥5.

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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