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Coatomic connected groups. (English. Russian original) Zbl 0712.22006

Sib. Math. J. 29, No. 3, 447-451 (1988); translation from Sib. Mat. Zh. 29, No. 3(169), 137-141 (1988).
The authors proves that in any nontrivial connected locally compact group there is a closed subgroup that is not an intersection of maximal closed subgroups. This is a solution of Problem VII.13b from the collection Unsolved problems in topological algebra [Preprint, Kishinev (1985)]. The author uses facts from his paper with G. A. Margulis [J. Algebra 69, No.1, 1-23 (1981; Zbl 0457.20046)].

MSC:

22D05 General properties and structure of locally compact groups

Citations:

Zbl 0457.20046
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References:

[1] Unsolved Problems in Topological Algebra [in Russian], Shtiintsa, Kishinev (1985).
[2] M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], Nauka, Moscow (1982). · Zbl 0508.20001
[3] A. Borel, Linear Algebraic Groups [Russian translation], Mir, Moscow (1972). · Zbl 0235.22017
[4] L. S. Pontryagin, Continuous Groups [in Russian], Nauka, Moscow (1973).
[5] G. A. Margulis and G. A. Soifer, ?Maximal subgroups of infinite index in finitely generated linear groups,? J. Algebra,69, No. 1, 1-23 (1981). · Zbl 0457.20046 · doi:10.1016/0021-8693(81)90123-X
[6] M. Ragunatan, Discrete Subgroups of Lie Groups [Russian translation], Mir, Moscow (1977).
[7] A. Borel and J. Tits, ?Reductive groups,? Matematika, Sb. Perevodov,11, No. 1, 43-111 (1967).
[8] V. P. Platonov, ?To the problem of maximal arithmetic groups,? Dokl. Akad. Nauk SSSR,200, No. 3, 530-533 (1971).
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