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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Blocks of central $p$-group extensions


Authors: Shigeo Koshitani and Naoko Kunugi
Journal: Proc. Amer. Math. Soc. 133 (2005), 21-26
MSC (2000): Primary 20C20, 20C05, 20C11
Published electronically: July 26, 2004
MathSciNet review: 2085148
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Abstract: Let $G$ and $G'$ be finite groups that have a common central $p$-subgroup $Z$ for a prime number $p$, and let ${\overline{A}}$ and ${\overline{A'}}$ respectively be $p$-blocks of $G/Z$ and $G'/Z$ induced by $p$-blocks $A$ and $A'$respectively of $G$ and $G'$, both of which have the same defect group. We prove that if ${\overline{A}}$ and ${\overline{A'}}$ are Morita equivalent via a certain special $({\overline{A}}, {\overline{A'}})$-bimodule, then such a Morita equivalence lifts to a Morita equivalence between $A$ and $A'$.


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Additional Information

Shigeo Koshitani
Affiliation: Department of Mathematics, Faculty of Science, Chiba University, Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan
Email: koshitan@math.s.chiba-u.ac.jp

Naoko Kunugi
Affiliation: Department of Mathematics, Aichi University of Education, Hirosawa, Igaya-cho, Kariya, 448-8542, Japan
Email: nkunugi@auecc.aichi-edu.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07509-4
PII: S 0002-9939(04)07509-4
Keywords: $p$-block, Morita equivalence, central extension
Received by editor(s): April 25, 2003
Received by editor(s) in revised form: September 8, 2003
Published electronically: July 26, 2004
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2004 American Mathematical Society