Characterizations of the solvable radical
Authors:
Paul Flavell, Simon Guest and Robert Guralnick
Journal:
Proc. Amer. Math. Soc. 138 (2010), 11611170
MSC (2010):
Primary 20F14, 20D10
Published electronically:
December 2, 2009
MathSciNet review:
2578510
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Abstract: We prove that there exists a constant with the property: if is a conjugacy class of a finite group such that every elements of generate a solvable subgroup, then generates a solvable subgroup. In particular, using the Classification of Finite Simple Groups, we show that we can take . We also present proofs that do not use the Classification Theorem. The most direct proof gives a value of . By lengthening one of our arguments slightly, we obtain a value of .
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Additional Information
Paul Flavell
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, United Kingdom
Email:
P.J.Flavell@bham.ac.uk
Simon Guest
Affiliation:
Department of Mathematics, Baylor University, One Bear Place #97328, Waco, Texas 767987328
Email:
Simon_Guest@baylor.edu
Robert Guralnick
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, California 900892532
Email:
guralnic@usc.edu
DOI:
http://dx.doi.org/10.1090/S0002993909100667
Keywords:
Solvable radical,
generation by conjugates
Received by editor(s):
August 28, 2008
Published electronically:
December 2, 2009
Additional Notes:
The second and third authors were partially supported by NSF grant DMS 0653873.
Communicated by:
Jonathan I. Hall
Article copyright:
© Copyright 2009
American Mathematical Society
