Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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 $ p$-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 $ p$-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 $ \mathcal{O}^*$-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, $ G$-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.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia