On the Dade character correspondence and isotypies between blocks of finite groups
Atumi Watanabe
Source: Osaka J. Math. Volume 47, Number 3
(2010), 817-837.
Abstract
In [3] Dade generalized the Glauberman character correspondence. In [13] Tasaka showed that the Dade correspondence induces an isotypy between blocks of finite groups under some assumptions. In this paper we obtain a generalization of [13], Theorem 5.5.
First Page:
Show
Hide
Primary Subjects:
20C20
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ojm/1285334476
Zentralblatt MATH identifier: 05810244
Mathematical Reviews number (MathSciNet): MR2768803
References
M. Broué: Isométries parfaites, types de blocs, catégories dérivées, Astérisque 181--182 (1990), 61--92.
Mathematical Reviews (MathSciNet): MR1051243
E.C. Dade: Isomorphisms of Clifford extensions, Ann. of Math. (2) 92 (1970), 375--433.
Mathematical Reviews (MathSciNet): MR269750
Digital Object Identifier: doi:10.2307/1970626
JSTOR: links.jstor.org
E.C. Dade: A new approach to Glauberman's correspondence, J. Algebra 270 (2003), 583--628.
Mathematical Reviews (MathSciNet): MR2019631
Zentralblatt MATH: 1037.20004
Digital Object Identifier: doi:10.1016/j.jalgebra.2002.11.002
G. Glauberman: Correspondences of characters for relatively prime operator groups, Canad. J. Math. 20 (1968), 1465--1488.
Mathematical Reviews (MathSciNet): MR232866
M. Hall Jr.: The Theory of Groups, Macmillan, New York, 1959.
Mathematical Reviews (MathSciNet): MR103215
M.E. Harris: Glauberman-Watanabe corresponding $p$-blocks of finite groups with normal defect groups are Morita equivalent, Trans. Amer. Math. Soc. 357 (2005), 309--335.
Mathematical Reviews (MathSciNet): MR2098097
Zentralblatt MATH: 1081.20011
Digital Object Identifier: doi:10.1090/S0002-9947-04-03478-6
A. Hida and S. Koshitani: Morita equivalent blocks in non-normal subgroups and $p$-radical blocks in finite groups, J. London Math. Soc. (2) 59 (1999), 541--556.
Mathematical Reviews (MathSciNet): MR1709664
Zentralblatt MATH: 0922.20016
Digital Object Identifier: doi:10.1112/S0024610799007139
H. Horimoto: The Glauberman-Dade correspondence and perfect isometries for principal blocks, preprint.
K. Iizuka, F. Ohmori and A. Watanabe: A Remark on the Representations of Finite Groups VI, Memoirs of Fac. of General Education, Kumamoto Univ., Ser. of Natural Sci., 18, 1983, (Japanese).
S. Koshitani and G.O. Michler: Glauberman correspondence of $p$-blocks of finite groups, J. Algebra 243 (2001), 504--517.
Mathematical Reviews (MathSciNet): MR1850660
Zentralblatt MATH: 1002.20009
Digital Object Identifier: doi:10.1006/jabr.2001.8777
B. Külshammer: Crossed products and blocks with normal defect groups, Comm. Algebra 13 (1985), 147--168.
Mathematical Reviews (MathSciNet): MR768092
Zentralblatt MATH: 0551.20004
Digital Object Identifier: doi:10.1080/00927878508823154
H. Nagao and Y. Tsushima: Representations of Finite Groups, Academic Press, Boston, MA, 1989.
Mathematical Reviews (MathSciNet): MR998775
Zentralblatt MATH: 0673.20002
F. Tasaka: On the isotypy induced by the Glauberman--Dade correspondence between blocks of finite groups, J. Algebra 319 (2008), 2451--2470.
Mathematical Reviews (MathSciNet): MR2388316
Zentralblatt MATH: 1194.20009
Digital Object Identifier: doi:10.1016/j.jalgebra.2007.12.017
F. Tasaka: A note on the Glauberman--Watanabe corresponding blocks of finite groups with normal defect groups, Osaka J. Math. 46 (2009), 327--352.
Mathematical Reviews (MathSciNet): MR2549590
Zentralblatt MATH: 05578933
Project Euclid: euclid.ojm/1245415673
J. Thévenaz: $G$-Algebras and Modular Representation Theory, Oxford Univ. Press, New York, 1995.
Mathematical Reviews (MathSciNet): MR1365077
A. Watanabe: The Glauberman character correspondence and perfect isometries for blocks of finite groups, J. Algebra 216 (1999), 548--565.
Mathematical Reviews (MathSciNet): MR1692989
Zentralblatt MATH: 0936.20006
Digital Object Identifier: doi:10.1006/jabr.1998.7779
2013 © Osaka University and Osaka City University, Departments of Mathematics
Osaka Journal of Mathematics
