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Some almost connected locally compact groups whose group topology is determined by the bounded structure

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It is proved that the topology of an almost connected locally compact group whose quotient group by the identity component is finitely generated and the identity component is a perfect connected locally compact group is determined by the bounded structure in the class of locally compact group topologies.

Abstract

It is proved that the topology of an almost connected locally compact group whose quotient group by the identity component is finitely generated and the identity component is a perfect connected locally compact group is determined by the bounded structure in the class of locally compact group topologies.

참고문헌 (9)

  1. A. I. Shtern, "Rigidity of the topology on the linear perfect connected Lie groups", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 14(4), pp.395~398 (2011), 장전수학회
  2. A. I. Shtern, "Bounded structure and continuity for homomorphisms of perfect connected locally compact groups", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 15(3), pp.235~240 (2012), 장전수학회
  3. A. I. Shtern, "Stewart groups and a question of dieter remus", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 16(3), pp.437~440 (2013), 장전수학회
  4. N. W. Rickert, "Locally compact topologies for groups", Trans. Amer. Math. Soc, 126, pp.225~235 (1967)
  5. W. W. Comfort, "Pseudocompact group topologies and totally dense subgroups", Pacific J. Math, 100(1), pp.61~84 (1982)
  6. N. Nikolov, "Finite index subgroups in profinite groups", C. R. Math. Acad. Sci. Paris, 337(5), pp.303~308 (2003)
  7. J. S. Wilson, "Finite index subgroups and verbal subgroups in profinite groups", S´eminaire Bourbaki, 2009, pp.2010(1026) (2011), 387~408
  8. D. H. Lee, "Supplements for the identity component in locally compact groups", Math. Z, 104(1), pp.28~49 (1968)
  9. D. Hawley, "Compact group topologies for R", Proc. Amer. Math. Soc, 30(3), pp.566~572 (1971)

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