Geodesic
Commutators of Matrices with Prescribed Determinant
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 203-221

Voir la notice de l'article provenant de la source Cambridge University Press

Let K be a commutative field, let GL(n, K) be the multiplicative group of all non-singular n × n matrices with elements from K, and let SL(n, K) be the subgroup of GL(n, K) consisting of all matrices in GL(n, K) with determinant one. We denote the determinant of matrix A by |A|, the identity matrix by In, the companion matrix of polynomial p(λ) by C(p(λ)), and the transpose of A by AT . The multiplicative group of nonzero elements in K is denoted by K*. We let GF(pn) denote the finite field having pn elements. 
Thompson, R. C. Commutators of Matrices with Prescribed Determinant. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 203-221. doi: 10.4153/CJM-1968-019-0
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[1] 1. Thompson, R. C., Commutators in the special and general linear groups, Trans. Amer. Math. Soc, 101 (1961), 16–33. Google Scholar

[2] 2. Thompson, R. C., On matrix commutators, Portugal. Math., 21 (1962), 143–153. Google Scholar

[3] 3. Thompson, R. C., Commutators of matrices with coefficients from the field of two elements, Duke Math. J., 29 (1962), 367–374. Google Scholar

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