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Perfect Isometries and Isotypies for Blocks with Abelian Defect Groups and the Inertial Quotients Isomorphic toZ4×Z2

✍ Scribed by Yoko Usami

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
367 KB
Volume
181
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let b be a p-block of a finite group G with abelian defect group P and e a root Ž . Ž Ž . Ž .. of b in C P . If the inertial quotient E s N P, e rPиC P is isomorphic to G G G Z = = = = = Z and p P 7, then there is a perfect isometry from the group of generalized 4 2 characters of some twisted group algebra of the semidirect product of E and P onto the group of generalized characters of G in b, and, furthermore, b and its Ž . Brauer correspondent in N P are isotypic.

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