Brauer characters of 
- degree
Authors:
Mark L. Lewis and Hung P. Tong Viet
Journal:
Proc. Amer. Math. Soc. 145 (2017), 1891-1898
MSC (2010):
Primary 20C20; Secondary 20C15, 20B15
DOI:
https://doi.org/10.1090/proc/13352
Published electronically:
January 26, 2017
MathSciNet review:
3611305
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We show that if 
is a prime and 
is a finite 
-solvable group satisfying the condition that a prime 
divides the degree of no irreducible 
-Brauer character of 
, then the normalizer of some Sylow 
-subgroup of 
meets all the conjugacy classes of 
-regular elements of 
.
- [1] Timothy C. Burness and Hung P. Tong-Viet, Derangements in primitive permutation groups, with an application to character theory, Q. J. Math. 66 (2015), no. 1, 63–96. MR 3356280, https://doi.org/10.1093/qmath/hau020
- [2] Burton Fein, William M. Kantor, and Murray Schacher, Relative Brauer groups. II, J. Reine Angew. Math. 328 (1981), 39–57. MR 636194, https://doi.org/10.1515/crll.1981.328.39
- [3] George Glauberman, Fixed points in groups with operator groups, Math. Z. 84 (1964), 120–125. MR 162866, https://doi.org/10.1007/BF01117119
- [4] I. M. Isaacs, Thomas Michael Keller, Mark L. Lewis, and Alexander Moretó, Transitive permutation groups in which all derangements are involutions, J. Pure Appl. Algebra 207 (2006), no. 3, 717–724. MR 2265547, https://doi.org/10.1016/j.jpaa.2005.11.005
- [5] C. Jordan, Recherches sur les substitutions, J. Math. Pures Appl. (Liouville) 17 (1872), 351-367.
- [6] Frank Lübeck, Small degree representations of finite Chevalley groups in defining characteristic, LMS J. Comput. Math. 4 (2001), 135–169. MR 1901354, https://doi.org/10.1112/S1461157000000838
- [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] Olaf Manz and Thomas R. Wolf, Brauer characters of 𝑞’-degree in 𝑝-solvable groups, J. Algebra 115 (1988), no. 1, 75–91. MR 937602, https://doi.org/10.1016/0021-8693(88)90283-9
- [9] G. Navarro, Variations on the Itô-Michler theorem of character degrees, Rocky Mountain J. Math., to appear.
- [10] G. Navarro, Characters and blocks of finite groups, London Mathematical Society Lecture Note Series, vol. 250, Cambridge University Press, Cambridge, 1998. MR 1632299
- [11] Jean-Pierre Serre, On a theorem of Jordan, Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 4, 429–440. MR 1997347, https://doi.org/10.1090/S0273-0979-03-00992-3
-degree in 
-solvable groups, J. Algebra 115 (1988), no. 1, 75-91. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20C20, 20C15, 20B15
Retrieve articles in all journals with MSC (2010): 20C20, 20C15, 20B15
Additional Information
Mark L. Lewis
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
Email:
lewis@math.kent.edu
Hung P. Tong Viet
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
Email:
htongvie@math.kent.edu
DOI:
https://doi.org/10.1090/proc/13352
Keywords:
Brauer character degrees,
derangements
Received by editor(s):
April 12, 2016
Received by editor(s) in revised form:
June 28, 2016
Published electronically:
January 26, 2017
Communicated by:
Pham Huu Tiep
Article copyright:
© Copyright 2017
American Mathematical Society
