Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-24T19:56:43.124Z Has data issue: false hasContentIssue false
  • English
  • Français

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
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.

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.

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

References

1. Borel, A., Groupes linéaires algébriques, Ann. of Math., 64 (1956), 20–83.Google Scholar
2. Dixon, J. D., Complete reducibility in infinite groups, Can. J. Math., 16 (1964), 267–274.Google Scholar
3. Kaplansky, I., An introduction to differential algebra (Paris, 1957).Google Scholar
4. Rosenlicht, M., Some basic theorems on algebraic groups, Amer. J. Math., 78 (1956), 401–443.Google Scholar
5. Schur, I., Über Gruppen periodischer Substitutionen, Sitzungsber. Preuss. Akad. Wiss. (1911), 619–627.Google Scholar
6. Suprunenko, D., Soluble and nilpotent linear groups, Translations of Math. Monographs, 9 (1964).Google Scholar