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

 

A refinement of Green's theorem on the defect group of a $ P$-block


Author: T. Y. Lam
Journal: Proc. Amer. Math. Soc. 54 (1976), 45-48
MathSciNet review: 0387397
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Abstract | References | Additional Information

Abstract: Let $ D$ be the defect group of a $ p$-block of a finite group $ G$. Let $ P,Q$ be two $ p$-Sylow groups of $ G$ containing $ D$. Then there exist $ x,y,z \in {C_G}(z)$ such that: (i) $ z$ is $ p$-regular and $ D$ is a $ p$-Sylow group of $ {C_G}(z)$; (ii) $ D = {Q^x} \cap P = Q \cap {P^y}$; and (iii) $ z = xy$. This refines an earlier theorem of J. A. Green.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0387397-2
PII: S 0002-9939(1976)0387397-2
Keywords: $ p$-Sylow groups, defect groups, indecomposable modules, vertices, tame Sylow intersections
Article copyright: © Copyright 1976 American Mathematical Society