|
On the Glauberman correspondent of a block
Author(s):
Yuanyang
Zhou
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2641-2651.
MSC (2010):
Primary 20C15, 20C20
Posted:
March 19, 2010
MathSciNet review:
2644880
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper, we analyze the compatibility of Fong's reduction and the Glauberman correspondence of characters and then clarify that the -solvable hypothesis in a paper of Harris and Linckelmann is not necessary.
References:
-
- 1.
- M. Broué, Isométries parfaites, types de blocs, catégories dérivées. Astérisque No. 181-182 (1990), 61-92. MR 1051243 (91i:20006)
- 2.
- E. Dade, A new approach to Glauberman's correspondence. J. Algebra 270 (2003), no. 2, 583-628. MR 2019631 (2004j:20010)
- 3.
- Y. Fan and L. Puig, On blocks with nilpotent coefficient extensions. Algebr. Represent. Theory 1 (1998), no. 1, 27-73. MR 1654602 (2000e:20019a)
- 4.
- G. Glauberman, Correspondences of characters for relatively prime operator groups. Can. J. Math. 20 (1968), 1465-1488. MR 0232866 (38:1189)
- 5.
- M. E. Harris and M. Linckelmann, On the Glauberman and Watanabe correspondences for blocks of finite
-solvable groups. Trans. Amer. Math. Soc. 354 (2002), no. 9, 3435-3453. MR 1911507 (2003c:20008) - 6.
- I. M. Isaacs, Character theory of finite groups. Academic Press, New York, 1976. MR 0460423 (57:417)
- 7.
- L. Puig, Nilpotent blocks and their source algebras. Invent. Math. 93 (1988), 77-116. MR 943924 (89e:20023)
- 8.
- L. Puig, Notes on
-groups, preprint, 1998. - 9.
- A. Watanabe, The Glauberman character correspondence and perfect isometries for blocks of finite groups. J. Algebra 216 (1999), 548-565. MR 1692989 (2000f:20015)
- 10.
- J. Thévenaz,
-algebras and modular representation theory. Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995. MR 1365077 (96j:20017)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2010):
20C15, 20C20
Retrieve articles in all Journals with
MSC (2010):
20C15, 20C20
Additional Information:
Yuanyang
Zhou
Affiliation:
Department of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, People's Republic of China
Email:
zhouyy74@163.com
DOI:
10.1090/S0002-9939-10-10320-7
PII:
S 0002-9939(10)10320-7
Keywords:
Characters,
blocks,
the Glauberman correspondent.
Received by editor(s):
May 14, 2009
Posted:
March 19, 2010
Communicated by:
Jonathan I. Hall
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|