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The Algebra of Dimension-Linking Operators

Published online by Cambridge University Press:  20 November 2018

R. H. Bruck
R. H. Bruck*
Affiliation:
University of Wisconsin, Madison, Wisconsin
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In the course of preparing a book on group theory [1] with special reference to the Restricted Burnside Problem and allied problems I stumbled upon the concept of a dimension-linking operator. Later, when I lectured to the Third Summer Institute of the Australian Mathematical Society [2], G. E. Wall raised the question whether the dimension-linking operators could be made into a ring by introduction of a suitable definition of multiplication. The answer was easily found to be affirmative; the result wasthat the theory of dimen sion-linking operators became exceedingly simple.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 2 , March 1965 , pp. 203 - 222
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Bruck, R. H., What Makes a Group Finite? A book being written under contract with Prentice-Hall.Google Scholar
2. Bruck, R. H., Engel conditions in groups and related questions. Mimeographed notes based on a series of 11 lectures delivered (during Jan. 8 - Jan. 22, 1963) to the Third Summer Research Institute of the Australian Mathematical Society, meeting Jan. 8 - Feb. 15, 1963 in Canberra A. C. T.Google Scholar
3. Higman, Graham, On a conjecture of Nagata, Proc. Cambridge Phil. Soc. 52(1956), 1–4.Google Scholar
4. Heineken, Hermann, Endomorphismenringe und engelsche Elemente, Archiv der Math. 13 (1962), 29–37.Google Scholar