The sparsity of Bruhat decomposition factors of nonsingular matrices

1996 ◽  
Vol 79 (3) ◽  
pp. 1035-1042
Author(s):  
L. Yu. Kolotilina
Keyword(s):  
Bruhat Decomposition ◽  
Nonsingular Matrices

scholarly journals A Bruhat decomposition of the group Sl∗(2,A)

2003 ◽  
Vol 262 (2) ◽  
pp. 401-412 ◽  
Author(s):  
José Pantoja ◽  
Jorge Soto-Andrade
Keyword(s):  
Bruhat Decomposition

scholarly journals A factorization of totally nonsingular matrices over a ring with identity

2000 ◽  
Vol 304 (1-3) ◽  
pp. 161-171 ◽  
Author(s):  
Miroslav Fiedler ◽  
Thomas L. Markham
Keyword(s):  
Nonsingular Matrices

Bruhat decomposition for long root tori in Chevalley groups

1991 ◽  
Vol 57 (6) ◽  
pp. 3453-3458 ◽  
Author(s):  
N. A. Vavilov ◽  
A. A. Semenov
Keyword(s):  
Bruhat Decomposition ◽  
Chevalley Groups

scholarly journals Finite automorphism groups of laminated near-rings

1983 ◽  
Vol 26 (3) ◽  
pp. 297-306 ◽  
Author(s):  
K. D. Magill ◽  
P. R. Misra ◽  
U. B. Tewari
Keyword(s):  
Finite Group ◽  
Linear Group ◽  
Complex Plane ◽  
Finite Groups ◽  
Automorphism Groups ◽  
The Other ◽  
Complex Polynomial ◽  
Infinite Groups ◽  
Nonsingular Matrices ◽  
A Finite Group

In [3] we initiated our study of the automorphism groups of a certain class of near-rings. Specifically, let P be any complex polynomial and let P denote the near-ring of all continuous selfmaps of the complex plane where addition of functions is pointwise and the product fg of two functions f and g in P is defined by fg=f∘P∘g. The near-ring P is referred to as a laminated near-ring with laminating element P. In [3], we characterised those polynomials P(z)=anzn + an−1zn−1 +…+a0 for which Aut P is a finite group. We are able to show that Aut P is finite if and only if Deg P≧3 and ai ≠ 0 for some i ≠ 0, n. In addition, we were able to completely determine those infinite groups which occur as automorphism groups of the near-rings P. There are exactly three of them. One is GL(2) the full linear group of all real 2×2 nonsingular matrices and the other two are subgroups of GL(2). In this paper, we begin our study of the finite automorphism groups of the near-rings P. We get a result which, in contrast to the situation for the infinite automorphism groups, shows that infinitely many finite groups occur as automorphism groups of the near-rings under consideration. In addition to this and other results, we completely determine Aut P when the coefficients of P are real and Deg P = 3 or 4.

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