Large character degrees of solvable $3’$-groups
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Abstract:
We prove that if $G$ is a finite solvable group and $3 \nmid |G:\mathbf {F}(G)|$, then the index of the Fitting subgroup of $G$ is at most the square of the largest irreducible character degree of $G$.References
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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
- 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
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 3171-3173
- MSC (2010): Primary 20C15
- DOI: https://doi.org/10.1090/S0002-9939-2011-10735-4
- MathSciNet review: 2811271