This article aims to describe the element structure of the special ... * Element structure of special linear group over a finite field ... ...
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This article aims to discuss the element structure of special linear ... * Element structure of special linear group of degree two over a field: ... ...
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Let R be a commutative unital ring and n be a natural number. The ... Here, the determinant for a matrix is defined in the usual way as ... ...
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Suppose G = GL(n,k) is the fact about::general linear group over a ... x^n is a surjective map from k to itself. In particular: ... ...
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(i.e., commutator subgroup) of the general linear group GL_n(k) (the ... In other words, the only case where the result does not hold is when ... ...
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Let n be a natural number. The special linear group over integers ... * It is the defining ingredient::special linear group SL(n,R) where ... ...
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Let R be any commutative unital ring and SL(2,R) be the special linear ... In other words, for any matrix A \in SL(2,R):
(A^t)^{-1} = \begin{pmatrix} ... ...
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number. Let G = GL(n,k) be the fact about::general linear group. Then, G is ... * Projective general linear group implies every element is automorphic ... ...
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Let k be a field and G := SL(2,k) be the fact about::special linear ... class-inverting automorphism: conjugation in GL(2,k) by the matrix \begin{pmatrix} ... ...
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G = PSL(n,k) be the fact about::projective special linear group of degree n ... * General linear group implies every element is automorphic to its inverse ... ...
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This article discusses the element structure of the general linear ... ===Other linear groups of degree four===
* Element structure of special ... ...
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number. Let G = SL(n,k) be the fact about::special linear group. Then, G is ... * General linear group implies every element is automorphic to its inverse ... ...
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The fact about::orthogonal group over reals O(n,\R) over the field ... Note that the statement is not true if we replace the orthogonal group ... ...
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Let n be a natural number and k be a field. The special affine group ... It can be viewed as a subgroup of the general affine group, which ... ...
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of individual conjugacy classes for the general linear group of degree two ... In the formulas below, the field size is q. The characteristic of ... ...
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The symplectic group Sp(2m,k) is a perfect group if either of these ... In other words, the only exceptions are Sp(2,2), Sp(2,3), Sp(4,2). ... ...
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Let n be a natural number and k a field. The special linear group ... # It is the group of all invertible matrices of order n, having determinant ... ...
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A group having a class-inverting automorphism is a group for which ... * Weaker than::Ambivalent group
* Weaker than::Abelian group ... ...
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for the endomorphism structure of the general linear group of degree two ... In the formulas below, the field size is q. The characteristic of ... ...
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G = PGL(n,k) be the fact about::projective general linear group. Then, G is ... * Special linear group implies every element is automorphic to its inverse ... ...
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