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Commutativity conditions for dmap solvable topological groups

A. I. Shtern
장전수학회 (Jangjeon Mathematical Society)|2012.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제15권 제2호|pp. 109-113|DOI 10.17777/pjms.2012.15.2.001

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참고문헌

키워드

Divisible grouplocally compact groupMAP (maximal almost periodic) topological groupDMAP topological groupsolvable topological group
주제분류수학

초록

By a DMAP topological group we mean a topological group which has sufficiently many (not necessarily continuous) finite-dimensional representations. In the paper, it is proved that a solvable DMAP topological group all of whose composition factors are divisible is commutative, and some consequences of this fact are indicated.

Abstract

By a DMAP topological group we mean a topological group which has sufficiently many (not necessarily continuous) finite-dimensional representations. In the paper, it is proved that a solvable DMAP topological group all of whose composition factors are divisible is commutative, and some consequences of this fact are indicated.

참고문헌 (14)

  1. W. W. Comfort, "Concerning connected, pseudocompact abelian groups", Topology Appl, 33(1), pp.21~25 (1989)
  2. K.-H. Hofmann, "The Structure of Compact Groups" (1998), de Gruyter
  3. A. I. Shtern, "Van der Waerden's continuity theorem for the commutator subgroups of connected Lie groups and Mishchenko's conjecture", Advanced Studies in Contemporary Mathematics, 13(2), pp.143~158 (2006), 장전수학회
  4. A. I. Shtern, "A version of the van der Waerden theorem and the proof of the Mishchenko conjecture for homomorphisms of locally compact groups", Izv. Ross. Akad. Nauk Ser. Mat, 72(1), pp.183~124 (2008)
  5. Alexander I. Shtern, "APPLICATIONS OF AUTOMATIC CONTINUITY RESULTS TO ANALOGS OF THE FREUDENTHAL–WEIL AND HOCHSCHILD THEOREMS", Advanced Studies in Contemporary Mathematics, 20(2), pp.203~212 (2010), 장전수학회
  6. Alexander I. Shtern, "VON NEUMANN KERNEL OF A CONNECTED LOCALLY COMPACT GROUP, REVISITED", Advanced Studies in Contemporary Mathematics, 20(3), pp.313~318 (2010), 장전수학회
  7. Shtern, "HOMOMORPHIC IMAGES OF CONNECTED LIE GROUPS IN COMPACT GROUPS", Advanced Studies in Contemporary Mathematics, 20(1), pp.1~6 (2010), 장전수학회
  8. A. I. Shtern, "Connected Lie groups having faithful locally bounded (not necessarily continuous) finite-dimensional representations", Russ. J. Math. Phys, 16(4), pp.566~567 (2009)
  9. Shtern, "FREUDENTHAL-WEIL THEOREM FOR ARBITRARY EMBEDDINGS OF CONNECTED LIE GROUPS IN COMPACT GROUPS", Advanced Studies in Contemporary Mathematics, 19(2), pp.157~164 (2009), 장전수학회
  10. A. I. Shtern, "Von Neumann kernels of connected Lie groups, revisited and refined", Russ. J. Math. Phys, 17(2), pp.262~266 (2010)
  11. A. I. Shtern, "Commutativity conditions for maximally almost periodic solvable topological groups", Proc. Jangjeon Math. Soc, 14(1), pp.1~ (2011)
  12. A. I. Shtern, "The structure of homomorphisms of connected locally compact groups into compact groups", Izv. Ross. Akad. Nauk Ser. Mat, 75(6), pp.195~122 (2011)
  13. J. von Neumann, "Almost periodic functions in a group", I, Trans. Amer. Math. Soc, 36, pp.445~492 (1934)
  14. A. Weil, "L’nt´egration dans les groupes topologiques et ses applications, 2nd ed" (1953), Act. Sc. Ind

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