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Dennis-Vaserstein type decompositions. (English. Russian original) Zbl 1215.20049

J. Math. Sci., New York 171, No. 3, 331-337 (2010); translation from Zap. Nauchn. Semin. POMI 375, 48-60 (2010).
Summary: A generalization of the Dennis-Vaserstein decomposition is proved for an arbitrary pair of maximal parabolic subgroups \(P_r\) and \(P_s\) in the general linear group \(\mathrm{GL}(n,R)\), provided that \(r-s\geq\mathrm{sr}(R)\). The usual Dennis-Vaserstein decomposition is the special case where \(r=n-1\), \(s=1\).

MSC:

20H25 Other matrix groups over rings
19B14 Stability for linear groups
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