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Commutators of Matrices with Prescribed Determinant

Published online by Cambridge University Press:  20 November 2018

R. C. Thompson
R. C. Thompson*
Affiliation:
University of California, Santa Barbara
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 203 - 221
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

The preparation of this paper was supported in part by the U.S. Air Force under Contract 698-65.

References

1. Thompson, R. C., Commutators in the special and general linear groups, Trans. Amer. Math. Soc, 101 (1961), 16–33.Google Scholar
2. Thompson, R. C., On matrix commutators, Portugal. Math., 21 (1962), 143–153.Google Scholar
3. Thompson, R. C., Commutators of matrices with coefficients from the field of two elements, Duke Math. J., 29 (1962), 367–374.Google Scholar