special linear group

Noun

 * 1)  For given field F and order n, the group of n×n matrices with determinant 1, with the group operations of matrix multiplication and matrix inversion.
 * 2) * 1998, F. Celler, C. R. Leedham-Green, A constructive recognition algorithm for the special linear group, Robert Curtis, Robert Wilson (editors), The Atlas of Finite Groups: Ten Years On,, 2003 Digitally Printed Edition, page 11,
 * In the first part of this note we present an algorithm to recognise constructively the special linear group.
 * In the first part of this note we present an algorithm to recognise constructively the special linear group.

Usage notes
The special linear group can be denoted SL(n, F) or SLn(F) — or, if the field is understood, SL(n) or SLn. It is a normal subgroup of the general linear group GL(n,F). In the cases that F is the field of real or of complex numbers, SL(n, F) is a Lie group.