Local-global principle for congruence subgroups of Chevalley groups

Himanee Apte; Alexei Stepanov

Open Mathematics (2014)

  • Volume: 12, Issue: 6, page 801-812
  • ISSN: 2391-5455

Abstract

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Suslin’s local-global principle asserts that if a matrix over a polynomial ring vanishes modulo the independent variable and is locally elementary then it is elementary. In this article we prove Suslin’s local-global principle for principal congruence subgroups of Chevalley groups. This result is a common generalization of the result of Abe for the absolute case and Apte, Chattopadhyay and Rao for classical groups. For the absolute case the localglobal principle was recently obtained by Petrov and Stavrova in the more general settings of isotropic reductive groups.

How to cite

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Himanee Apte, and Alexei Stepanov. "Local-global principle for congruence subgroups of Chevalley groups." Open Mathematics 12.6 (2014): 801-812. <http://eudml.org/doc/268946>.

@article{HimaneeApte2014,
abstract = {Suslin’s local-global principle asserts that if a matrix over a polynomial ring vanishes modulo the independent variable and is locally elementary then it is elementary. In this article we prove Suslin’s local-global principle for principal congruence subgroups of Chevalley groups. This result is a common generalization of the result of Abe for the absolute case and Apte, Chattopadhyay and Rao for classical groups. For the absolute case the localglobal principle was recently obtained by Petrov and Stavrova in the more general settings of isotropic reductive groups.},
author = {Himanee Apte, Alexei Stepanov},
journal = {Open Mathematics},
keywords = {Chevalley groups; Principal congruence subgroup; Local-global principle; Dilation principle; principal congruence subgroups; local-global principle; dilation principle},
language = {eng},
number = {6},
pages = {801-812},
title = {Local-global principle for congruence subgroups of Chevalley groups},
url = {http://eudml.org/doc/268946},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Himanee Apte
AU - Alexei Stepanov
TI - Local-global principle for congruence subgroups of Chevalley groups
JO - Open Mathematics
PY - 2014
VL - 12
IS - 6
SP - 801
EP - 812
AB - Suslin’s local-global principle asserts that if a matrix over a polynomial ring vanishes modulo the independent variable and is locally elementary then it is elementary. In this article we prove Suslin’s local-global principle for principal congruence subgroups of Chevalley groups. This result is a common generalization of the result of Abe for the absolute case and Apte, Chattopadhyay and Rao for classical groups. For the absolute case the localglobal principle was recently obtained by Petrov and Stavrova in the more general settings of isotropic reductive groups.
LA - eng
KW - Chevalley groups; Principal congruence subgroup; Local-global principle; Dilation principle; principal congruence subgroups; local-global principle; dilation principle
UR - http://eudml.org/doc/268946
ER -

References

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