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Some Generalizations Of Burnsides Theorem

Published online by Cambridge University Press:  20 November 2018

N. A. Wiegmann
N. A. Wiegmann*
Affiliation:
Catholic University, Washington, D.C.
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1. Introduction. Burnside's Theorem in the theory of group representations states that a necessary and sufficient condition that a semigroup of matrices of degree n over the complex field be irreducible is that the semigroup contain n2 linearly independent matrices. In the course of dealing with sets of matrices with coefficients in a division ring, Brauer (1) obtained a generalization of this theorem which concerned irreducible semigroups with elements in a division ring.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 336 - 346
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Brauer, R., On sets of matrices with coefficients in a division ring, Trans. Amer. Math. Soc, 49(1941), 502–547.Google Scholar
2. Moore, E. H., General analysis, Part I, Memoirs of the American Philosophical Society, I (1935).Google Scholar
3. Wiegmarm, N. A., Some theorems on matrices with real quaternion elements, Can. J. Math., 7 (1955), 191–201.Google Scholar