Blocks of defect of p-solvable groups

2015/01/14 by Yong Yang, Yang, Yong · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR

paper · pdf · doi:10.48550/arxiv.1501.03237

arXiv admin note: substantial text overlap with arXiv:1208.4022

arxiv created 2015/01/14 · openalex publication_date 2015/01/14 · arxiv updated 2015/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime such that p ≥ 5. Let G be a finite p-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:F(G)|_p ≤ p^5.5a. Let G be a finite p-solvable group with trivial maximal normal solvable subgroup and we denote |G|_p=pⁿ, then G contains a block of defect less than or equal to \lfloor \frac 2n 3 \rfloor.

Citations

• Blocks of small defect

Cited by

• On p-parts of character degrees and conjugacy class sizes of finite groups

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