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In mathematics, the special linear group SL of degree n over a field F is the set of n × n matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the general linear group given by the kernel of the determinant
where F is the multiplicative group of F.
These elements are "special" in that they form an algebraic subvariety of the general linear group – they satisfy a polynomial equation.
When F is a finite field of order q, the notation SL is sometimes used.
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