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On the nth root set of an element in a connected semisimple Lie group

Published online by Cambridge University Press:  24 October 2008

M. McCrudden
M. McCrudden
Affiliation:
University of Manchester
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Extract

For any group G and x ∈ G, and any n ∈ ℕ (the natural numbers) let

i.e. the set of all nth roots of x in G.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 86 , Issue 2 , September 1979 , pp. 219 - 226
Copyright
Copyright © Cambridge Philosophical Society 1979

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References

REFERENCES

(1)Bourbaki, N.Elements of mathematics, Lie groups and Lie algebras, part 1 (Addison Wesley, 1975).Google Scholar
(2)Bourbaki, N.Elements de Mathématique, Groupes et Algèbres de Lie, chapters VII, VIII (Paris, Hermann, 1975).Google Scholar
(3)De Siebenthal, J.Sur les groupes de Lie compact non connexes. Comment. Math. Helv. 31 (1956/1957), 41–89.CrossRefGoogle Scholar
(4)Goto, M.On an integer associated with an algebraic group, J. Math. Soc. Japan 29 (1977), 161–163.CrossRefGoogle Scholar
(5)Hewitt, E. and Ross, K. A.Abstract harmonic analysis, vol. i (Berlin, Springer-Verlag, 1963).Google Scholar
(6)Hochschild, G.The structure of Lie groups (San Francisco, Holden-Day, 1965).Google Scholar
(7)Lai, H. L.Surjectivity of exponential map on semisimple Lie groups. J. Math. Soc. Japan 29 (1977).Google Scholar
(8)Mostow, G. D.On the fundamental group of a homogeneous space, Ann. of Math., 66, (1957), 249–255.CrossRefGoogle Scholar
(9)Steinberg, R.Conjugacy classes in algebraic groups. Lecture Notes in Mathematics, no. 366 (Springer-Verlag, 1974).CrossRefGoogle Scholar
(10)Warner, G.Harmonic analysis on semisimple Lie groups, vol. i (Springer-Verlag, 1972).Google Scholar