Brauer characters of $q’$- degree
HTML articles powered by AMS MathViewer
- by Mark L. Lewis and Hung P. Tong Viet
- Proc. Amer. Math. Soc. 145 (2017), 1891-1898
- DOI: https://doi.org/10.1090/proc/13352
- Published electronically: January 26, 2017
- PDF | Request permission
Corrigendum: Proc. Amer. Math. Soc. 150 (2022), 5023-5024.
Abstract:
We show that if $p$ is a prime and $G$ is a finite $p$-solvable group satisfying the condition that a prime $q$ divides the degree of no irreducible $p$-Brauer character of $G$, then the normalizer of some Sylow $q$-subgroup of $G$ meets all the conjugacy classes of $p$-regular elements of $G$.References
- 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, DOI 10.1093/qmath/hau020
- Burton Fein, William M. Kantor, and Murray Schacher, Relative Brauer groups. II, J. Reine Angew. Math. 328 (1981), 39–57. MR 636194, DOI 10.1515/crll.1981.328.39
- George Glauberman, Fixed points in groups with operator groups, Math. Z. 84 (1964), 120–125. MR 162866, DOI 10.1007/BF01117119
- 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, DOI 10.1016/j.jpaa.2005.11.005
- C. Jordan, Recherches sur les substitutions, J. Math. Pures Appl. (Liouville) 17 (1872), 351–367.
- Frank Lübeck, Small degree representations of finite Chevalley groups in defining characteristic, LMS J. Comput. Math. 4 (2001), 135–169. MR 1901354, DOI 10.1112/S1461157000000838
- 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, DOI 10.1017/CBO9780511525971
- 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, DOI 10.1016/0021-8693(88)90283-9
- G. Navarro, Variations on the Itô-Michler theorem of character degrees, Rocky Mountain J. Math., to appear.
- G. Navarro, Characters and blocks of finite groups, London Mathematical Society Lecture Note Series, vol. 250, Cambridge University Press, Cambridge, 1998. MR 1632299, DOI 10.1017/CBO9780511526015
- Jean-Pierre Serre, On a theorem of Jordan, Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 4, 429–440. MR 1997347, DOI 10.1090/S0273-0979-03-00992-3
Bibliographic Information
- Mark L. Lewis
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- MR Author ID: 363107
- Email: lewis@math.kent.edu
- Hung P. Tong Viet
- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- MR Author ID: 772164
- Email: htongvie@math.kent.edu
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1891-1898
- MSC (2010): Primary 20C20; Secondary 20C15, 20B15
- DOI: https://doi.org/10.1090/proc/13352
- MathSciNet review: 3611305