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Parabolic subgroups of Vershik-Kerov's group

Author: Waldemar Holubowski
Journal: Proc. Amer. Math. Soc. 130 (2002), 2579-2582
MSC (2000): Primary 20H25, 20E15
Published electronically: March 15, 2002
MathSciNet review: 1900864
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Abstract: In this note we show that all parabolic subgroups of Vershik-Kerov's group $GLB(R)$ (i.e. subgroups containing $T(\infty,R)$--the group of infinite dimensional upper triangular matrices) are net subgroups for a wide class of semilocal rings $R$.

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Additional Information

Waldemar Holubowski
Affiliation: Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

Keywords: Parabolic subgroup, net subgroup
Received by editor(s): March 22, 2001
Received by editor(s) in revised form: May 10, 2001
Published electronically: March 15, 2002
Dedicated: Dedicated to Z. I. Borevich (1922-1995)
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2002 American Mathematical Society