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Some Generalizations Of Burnsides Theorem
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1957