Large character degrees of solvable -groups

Author:
Yong Yang

Journal:
Proc. Amer. Math. Soc. **139** (2011), 3171-3173

MSC (2010):
Primary 20C15

Published electronically:
January 20, 2011

MathSciNet review:
2811271

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if is a finite solvable group and , then the index of the Fitting subgroup of is at most the square of the largest irreducible character degree of .

**1.**Alberto Espuelas,*Large character degrees of groups of odd order*, Illinois J. Math.**35**(1991), no. 3, 499–505. MR**1103682****2.**Silvio Dolfi,*Intersections of odd order Hall subgroups*, Bull. London Math. Soc.**37**(2005), no. 1, 61–66. MR**2105819**, 10.1112/S0024609304003807**3.**Silvio Dolfi,*Large orbits in coprime actions of solvable groups*, Trans. Amer. Math. Soc.**360**(2008), no. 1, 135–152 (electronic). MR**2341997**, 10.1090/S0002-9947-07-04155-4**4.**Silvio Dolfi and Enrico Jabara,*Large character degrees of solvable groups with abelian Sylow 2-subgroups*, J. Algebra**313**(2007), no. 2, 687–694. MR**2329564**, 10.1016/j.jalgebra.2006.12.004**5.**David Gluck,*The largest irreducible character degree of a finite group*, Canad. J. Math.**37**(1985), no. 3, 442–451. MR**787111**, 10.4153/CJM-1985-026-8**6.**Alexander Moretó and Thomas R. Wolf,*Orbit sizes, character degrees and Sylow subgroups*, Adv. Math.**184**(2004), no. 1, 18–36. MR**2047847**, 10.1016/S0001-8708(03)00093-8**7.**Olaf Manz and Thomas R. Wolf,*Representations of solvable groups*, London Mathematical Society Lecture Note Series, vol. 185, Cambridge University Press, Cambridge, 1993. MR**1261638****8.**Yong Yang,*Orbits of the actions of finite solvable groups*, J. Algebra**321**(2009), no. 7, 2012–2021. MR**2494754**, 10.1016/j.jalgebra.2008.12.016**9.**Yong Yang,*Regular orbits of finite primitive solvable groups*, J. Algebra**323**(2010), no. 10, 2735–2755. MR**2609172**, 10.1016/j.jalgebra.2010.02.031**10.**Yong Yang, `Regular orbits of finite primitive solvable groups, II', Journal of Algebra, to appear.

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Additional Information

**Yong Yang**

Affiliation:
Department of Mathematics, Texas State University at San Marcos, San Marcos, Texas 78666

Email:
yang@txstate.edu

DOI:
https://doi.org/10.1090/S0002-9939-2011-10735-4

Received by editor(s):
March 17, 2010

Received by editor(s) in revised form:
July 22, 2010, and August 18, 2010

Published electronically:
January 20, 2011

Communicated by:
Jonathan I. Hall

Article copyright:
© Copyright 2011
American Mathematical Society