Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-02-05T03:09:09.758Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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