scholarly journals Chevalley groups over commutative rings

1971 ◽  
Vol 77 (2) ◽  
pp. 247-253 ◽  
Author(s):  
Michael R. Stein
Keyword(s):  
Commutative Rings ◽  
Chevalley Groups

Chevalley groups over commutative rings: I. Elementary calculations

1996 ◽  
Vol 45 (1) ◽  
pp. 73-113 ◽  
Author(s):  
Nikolai Vavilov ◽  
Eugene Plotkin
Keyword(s):  
Commutative Rings ◽  
Chevalley Groups

scholarly journals Decompositions of congruence subgroups of Chevalley groups

2018 ◽  
Vol 28 (06) ◽  
pp. 935-958
Author(s):  
Sergey Sinchuk ◽  
Andrei Smolensky
Keyword(s):  
Commutative Rings ◽  
Principal Congruence ◽  
Congruence Subgroups ◽  
Chevalley Groups ◽  
Type Formula

We formulate and prove relative versions of several decompositions known in the theory of Chevalley groups over commutative rings. These decompositions are used to obtain factorizations in terms of subsystem subgroups of type [Formula: see text] and upper estimates of the width of principal congruence subgroups with respect to Tits–Vaserstein generators.

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