Subgroups of the General Linear Group That Contain Elementary Subgroup Over a Rank 2 Commutative Ring Extension

2018 ◽  
Vol 234 (2) ◽  
pp. 256-267
Author(s):  
T. N. Hoi ◽  
N. H. T. Nhat
Keyword(s):  
Commutative Ring ◽  
Linear Group ◽  
General Linear Group ◽  
General Linear ◽  
Ring Extension ◽  
Elementary Subgroup ◽  
Rank 2

A note on the subnormal structure of general linear groups

1990 ◽  
Vol 107 (2) ◽  
pp. 193-196 ◽  
Author(s):  
N. A. Vavilov
Keyword(s):  
Commutative Ring ◽  
Linear Group ◽  
General Linear Group ◽  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
Elementary Subgroup ◽  
Subnormal Structure

The purpose of this note is to improve results of J. S. Wilson[12] and L. N. Vaserstein [10] concerning the subnormal structure of the general linear group G = GL (n, R) of degree n ≽ 3 over a commutative ring R. To do this we sharpen results of J. S. Wilson[12], A. Bak[1] and L. N. Vaserstein[10] on subgroups normalized by a relative elementary subgroup. It should be said also that (especially for the case n = 3) our proof is very much simpler than that of[12, 10]. To formulate our results let us recall some notation.

Elementary symplectic orbits and improved K1-stability

2010 ◽  
Vol 7 (2) ◽  
pp. 389-403 ◽  
Author(s):  
Pratyusha Chattopadhyay ◽  
Ravi A. Rao
Keyword(s):  
Commutative Ring ◽  
Linear Group ◽  
Symplectic Group ◽  
General Linear Group ◽  
General Linear ◽  
Affine Algebras

AbstractIt is shown that the set of orbits of the action of the elementary symplectic group on all unimodular rows over a commutative ring of characteristic not 2 is identical with the set of orbits of the action of the corresponding elementary general linear group. This result is used to improve injective stability for K1 of the symplectic group over non-singular affine algebras.

scholarly journals Study of Graded Algebras and General Linear Group with Lie Superalgebras and R-Algebra

2020 ◽  
Vol 68 (1) ◽  
pp. 1-5
Author(s):  
Khondokar M Ahmed ◽  
SK Rasel ◽  
Jyoti Das ◽  
Saraban Tahura ◽  
Salma Nasrin
Keyword(s):  
Commutative Ring ◽  
Linear Group ◽  
General Linear Group ◽  
Lie Superalgebras ◽  
General Linear ◽  
Tensor Algebra ◽  
Graded Rings ◽  
Graded Algebras

Some elements of theory of Z2 graded rings, modules and algebras. Z2-graded tensor algebra, Lie superalgrbras and matrices with entries in a Z2-graded commutative ring are treated in our present paper. At last a Theorem 4.4.on the set of square matrices in the graded R-algebra , MR-[m I n] is established. Dhaka Univ. J. Sci. 68(1): 1-5, 2020 (January)

Representations induced from the Zelevinsky segment and discrete series in the half-integral case

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ivan Matić
Keyword(s):  
Linear Group ◽  
Local Field ◽  
General Linear Group ◽  
Discrete Series ◽  
Series Representation ◽  
General Linear ◽  
Composition Series ◽  
Induced Representations ◽  
Discrete Series Representation

AbstractLet {G_{n}} denote either the group {\mathrm{SO}(2n+1,F)} or {\mathrm{Sp}(2n,F)} over a non-archimedean local field of characteristic different than two. We study parabolically induced representations of the form {\langle\Delta\rangle\rtimes\sigma}, where {\langle\Delta\rangle} denotes the Zelevinsky segment representation of the general linear group attached to the segment Δ, and σ denotes a discrete series representation of {G_{n}}. We determine the composition series of {\langle\Delta\rangle\rtimes\sigma} in the case when {\Delta=[\nu^{a}\rho,\nu^{b}\rho]} where a is half-integral.

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