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Perfect Isometries for Principal Blocks with Abelian Defect Groups and Elementary Abelian 2-Inertial Quotients

✍ Scribed by Yoko Usami

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 400 KB
Volume: 196
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7094

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✦ Synopsis

Let b be the principal p-block of a finite group G with an abelian defect group Ž . Ž Ž . Ž .. P and e a root of b in C P . If the inertial quotient E s N P, e rPиC P is G G G

Ž . an elementary abelian 2-group respectively, a dihedral group of order 8 and Ž . p / 3, then b and its Brauer correspondent, considered as blocks of G and N P G are isotypic and, in particular, there is a perfect isometry between them.

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