A refinement of Green’s theorem on the defect group of a $P$-block
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- by T. Y. Lam PDF
- Proc. Amer. Math. Soc. 54 (1976), 45-48 Request permission
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.References
- J. L. Alperin, Sylow intersections and fusion, J. Algebra 6 (1967), 222–241. MR 215913, DOI 10.1016/0021-8693(67)90005-1
- J. A. Green, Blocks of modular representations, Math. Z. 79 (1962), 100–115. MR 141717, DOI 10.1007/BF01193108
- James A. Green, Some remarks on defect groups, Math. Z. 107 (1968), 133–150. MR 233901, DOI 10.1007/BF01111026
- John G. Thompson, Defect groups are Sylow intersections, Math. Z. 100 (1967), 146. MR 213432, DOI 10.1007/BF01110791
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 45-48
- DOI: https://doi.org/10.1090/S0002-9939-1976-0387397-2
- MathSciNet review: 0387397