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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Principal $2$-blocks of the simple groups of Ree type

Authors: Peter Landrock and Gerhard O. Michler
Journal: Trans. Amer. Math. Soc. 260 (1980), 83-111
MSC: Primary 20C20; Secondary 16A64, 20C30
MathSciNet review: 570780
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Abstract: The decomposition numbers in characteristic 2 of the groups of Ree type are determined, as well as the Loewy and socle series of the indecomposable projective modules. Moreover, we describe the Green correspondents of the simple modules. As an application of this and similar works on other simple groups with an abelian Sylow 2-subgroup, all of which have been classified apart from those considered in the present paper, we show that the Loewy length of an indecomposable projective module in the principal block of any finite group with an abelian Sylow 2-subgroup of order ${2^n}$ is bounded by $\max \{ 2n + 1, {2^n}\}$. This bound is the best possible.

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Keywords: Decomposition numbers, projective modules, Green correspondents, simple modules, groups of Ree type
Article copyright: © Copyright 1980 American Mathematical Society