The largest character degree and the Sylow subgroups of finite groups.

DOI10.1016/j.jalgebra.2003.02.009zbMath1062.20008OpenAlexW1966542212MaRDI QIDQ1879639

Guohua Qian, Wujie Shi

Publication date: 23 September 2004

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2003.02.009

zbMATH Keywords

degrees of irreducible charactersSylow subgroupscharacter degree bounds

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60)

Related Items (9)

The largest character degree, conjugacy class size and subgroups of finite groups ⋮ On finite groups with certain complemented p -subgroups ⋮ FINITE GROUPS WITH COMPLEMENTED 2-MINIMAL -SUBGROUPS ⋮ The largest conjugacy class size and the nilpotent subgroups of finite groups ⋮ The size of the largest conjugacy classes and the Sylow \(p\)-subgroups of finite groups ⋮ Bounding an Index by the Largest Character Degree of ap-Solvable Group ⋮ On the largest conjugacy class length of a finite group. ⋮ On Class Size of p-Singular Elements in Finite Groups ⋮ Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite group

Cites Work

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• Blocks of defect zero in finite simple groups of Lie type
• Automorphisms which centralize a Sylow p-subgroup
• Central elements in core-free groups
• Large orbits in actions of nilpotent groups
• A bound for $|G:\mathbf O_p(G)|_p$ in terms of the largest irreducible character degree of a finite $p$-solvable group $G$
• Notes on the largest irreducible character degree of a finite group

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