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On the involution classes of the linear groups GLn(K), SLn(K), PGLn(K), PSLn(K) over fields of characteristic two

Published online by Cambridge University Press:  24 October 2008

R. H. Dye
R. H. Dye
Affiliation:
University of Newcastle upon Tyne
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Extract

1. Introduction. 1.1 In (5), (6) and (7) I have catalogued the classes of involutions of the orthogonal, symplectic and unitary groups over perfect fields of characteristic 2. So, too, were obtained the involution classes of the well-known relatives of these groups. For each group the relevant classes have simple and explicit descriptions in terms of the geometry of its setting, and an overall pattern can be seen.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 1 , July 1972 , pp. 1 - 6
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Albert, A. A.Modern higher algebra (Cambridge, 1938).Google Scholar
(2)Brandis, A.Über die multiplikative Struktur von Körpererweiterungen. Math. Zeit. 87 (1965), 71–73.CrossRefGoogle Scholar
(3)Dickson, L. E.Linear groups (Leipzig, 1901).Google Scholar
(4)Dieudonné, J.La geométrie des groupes classiques (2nd ed.Berlin, 1963).CrossRefGoogle Scholar
(5)Dye, R. H.On the conjugacy classes of involutions of the orthogonal groups over perfect fields of characteristic 2. Bull. London Math. Soc. 3 (1971), 61–66.Google Scholar
(6)Dye, R. H.On the conjugacy classes of involutions of the simple orthogonal groups over perfect fields of characteristic two. J. Algebra 18 (1971), 414–425.Google Scholar
(7)Dye, R. H. On the conjugacy classes of involutions of the unitary groups U m+1(K), SU m+1 (K), PU m+1 (K) PSU m+1 (K) over perfect fields of characteristic 2 (to appear).Google Scholar
(8)Jordan, C.Traité des substitutions (Paris, 1870).Google Scholar
(9)Segre, B.Lectures on modern geometry (Rome, 1961).Google Scholar
(10)Turnbull, H. W. and Aitken, A. C.The theory of canonical matrices (London, 1932).Google Scholar