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A Note on d-Groups

Published online by Cambridge University Press:  20 November 2018

B. A. F. Wehrfritz
B. A. F. Wehrfritz*
Affiliation:
Queen Mary College, University of London, London, England
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This note concerns subgroups of the general linear group GL(n, F), where n is finite and F algebraically closed, g ∈ GL(n, F) is called a d-element if there exists an x ∈ GL(w, F) such that x–1gx is diagonal, and a u-element if (g — 1)n = 0. A subgroup G of GL(n, F) is called a d-group (or a u-group) if every element of G is a d-element (or a u-element). In view of the Jordan decomposition of the elements of GL(n, F) into products of d-elements and u-elements it is important to know the structure of d-groups and u-groups, u-groups present very little difficulty and their structure is well known (1, 19.4), but d-groups seem to have a more complicated structure.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967, pp. 410 - 412
Copyright
Copyright © Canadian Mathematical Society 1967

References

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