On the existence of dense analytic subgroups

Zerling, David

doi:10.1090/S0002-9939-1978-0509256-6

On the existence of dense analytic subgroups
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by David Zerling

Proc. Amer. Math. Soc. 72 (1978), 566-570

DOI: https://doi.org/10.1090/S0002-9939-1978-0509256-6

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Abstract:

The purpose of this paper is to establish a necessary and sufficient condition for a connected Lie group to contain a proper dense connected Lie subgroup.

References

Dragomir Ž. Djoković, Three notes on real analytic groups, Tohoku Math. J. (2) 28 (1976), no. 3, 381–387. MR 430150, DOI 10.2748/tmj/1178240778
Morikuni Goto, Dense imbeddings of locally compact connected groups, Ann. of Math. (2) 61 (1955), 154–169. MR 65567, DOI 10.2307/1969626
Morikuni Goto, Analytic subgroups of $\textrm {GL}(n,\,\textbf {R})$, Tohoku Math. J. (2) 25 (1973), 197–199. MR 322099, DOI 10.2748/tmj/1178241378
Kenkichi Iwasawa, On some types of topological groups, Ann. of Math. (2) 50 (1949), 507–558. MR 29911, DOI 10.2307/1969548
M. Rajagopalan and H. Subrahmanian, Dense subgroups of locally compact groups, Colloq. Math. 35 (1976), no. 2, 289–292. MR 417325
David Zerling, Dense subgroups of Lie groups. II, Trans. Amer. Math. Soc. 246 (1978), 419–428. MR 515548, DOI 10.1090/S0002-9947-1978-0515548-1