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Large character degrees of solvable $ 3'$-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: We prove that if $ G$ is a finite solvable group and $ 3 \nmid \vert G:\mathbf{F}(G)\vert$, then the index of the Fitting subgroup of $ G$ is at most the square of the largest irreducible character degree of $ G$.


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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