Blocks of central -group extensions

Authors:
Shigeo Koshitani and Naoko Kunugi

Journal:
Proc. Amer. Math. Soc. **133** (2005), 21-26

MSC (2000):
Primary 20C20, 20C05, 20C11

DOI:
https://doi.org/10.1090/S0002-9939-04-07509-4

Published electronically:
July 26, 2004

MathSciNet review:
2085148

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let and be finite groups that have a common central -subgroup for a prime number , and let and respectively be -blocks of and induced by -blocks and respectively of and , both of which have the same defect group. We prove that if and are Morita equivalent via a certain special -bimodule, then such a Morita equivalence lifts to a Morita equivalence between and .

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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:
https://doi.org/10.1090/S0002-9939-04-07509-4

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