Blocks of small defect

2012/08/20 by Yong Yang, Yang, Yong · 1 citation
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1208.4022

arxiv created 2012/08/20 · arxiv updated 2012/08/21

Abstract

Let G be a finite solvable group, let p be a prime such that p ≥ 5 and O_p(G)=1, and we denote |G|_p=pⁿ, then G contains a block of defect less than or equal to \lfloor \frac 3n 5 \rfloor. Let G be a finite solvable group and let p^a be the largest power of p dividing χ(1) for an irreducible character χ of G, we show that |G:\bF(G)|_p ≤ p^3a for p ≥ 5.

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• Blocks of defect of p-solvable groups

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