Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Dense subgroups of Lie groups

Author: David Zerling
Journal: Proc. Amer. Math. Soc. 62 (1977), 349-352
MSC: Primary 22E20
MathSciNet review: 0435289
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let G be a dense analytic subgroup with compact center of an analytic group L. Then there exist closed vector subgroups W and U of G and a (CA) closed normal analytic subgroup M of G, which contains the center of G, such that $ G = MWU,MW \cap U = M \cap W = \{e\}$, and WU is a closed vector subgroup of G. Moreover, $ L = MW\bar U$, where MW is a closed normal analytic subgroup of L and $ \bar U$ is a toral group, such that $ MW \cap \bar U$ is finite.

References [Enhancements On Off] (What's this?)

  • [1] M. Goto, Analytic subgroups of $ {\text{GL}}(n,{\mathbf{R}})$, Tôhoku Math. J. (2) 25 (1973), 197-199. MR 48 #463. MR 0322099 (48:463)
  • [2] W. T. van Est, Dense imbeddings of Lie groups, Nederl. Akad. Wetensch. Proc. Ser. A 54 = Indag. Math. 13 (1951), 321-328. MR 13, 432. MR 0044530 (13:432c)
  • [3] D. Zerling, Some theorems on (CA) analytic groups, Trans. Amer. Math. Soc. 205 (1975), 181-192. MR 51 #802. MR 0364548 (51:802)
  • [4] -, Some theorems on (CA) analytic groups. II, Tôhoku Math. J. (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22E20

Retrieve articles in all journals with MSC: 22E20

Additional Information

PII: S 0002-9939(1977)0435289-3
Article copyright: © Copyright 1977 American Mathematical Society