Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Blocks with central product defect group $ D_{2^n}\ast C_{2^m}$


Author: Benjamin Sambale
Journal: Proc. Amer. Math. Soc. 141 (2013), 4057-4069
MSC (2010): Primary 20C15, 20C20
Published electronically: August 14, 2013
MathSciNet review: 3105851
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We determine the numerical invariants of blocks with defect group $ D_{2^n}\ast C_{2^m}\cong Q_{2^n}\ast C_{2^m}$ (central product), where $ n\ge 3$ and $ m\ge 2$. As a consequence, we prove Brauer's $ k(B)$-conjecture, Olsson's conjecture (and more generally Eaton's conjecture), Brauer's height zero conjecture, the Alperin-McKay conjecture, Alperin's weight conjecture and Robinson's ordinary weight conjecture for these blocks. Moreover, we show that the gluing problem has a unique solution in this case. This paper continues B. Sambale, Blocks with defect group $ D_{2^n}\times C_{2^m}$, J. Pure Appl. Algebra 216 (2012), 119-125.


References [Enhancements On Off] (What's this?)


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

Benjamin Sambale
Affiliation: Mathematisches Institut, Friedrich-Schiller-Universität, 07743 Jena, Germany
Email: benjamin.sambale@uni-jena.de

DOI: https://doi.org/10.1090/S0002-9939-2013-11938-6
Keywords: $2$-blocks, dihedral defect groups, Alperin's weight conjecture, ordinary weight conjecture
Received by editor(s): June 8, 2011
Received by editor(s) in revised form: February 1, 2012
Published electronically: August 14, 2013
Additional Notes: This work was partly supported by the Deutsche Forschungsgemeinschaft
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.