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COMMUTATIVITY CONDITIONS FOR MAXIMALLY ALMOST PERIODIC SOLVABLE TOPOLOGICAL GROUPS

A. I. Shtern
장전수학회 (Jangjeon Mathematical Society)|2011.01|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제14권 제1호|pp. 1-6|DOI 10.17777/pjms.2011.14.1.001

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초록

In the paper, it is proved that a connected MAP solvable topo-logical group is commutative and that an arcwise connected MAP prosolvable pro-Lie group is commutative. Thus, the solvable radical of any arcwise con-nected MAP pro-Lie group is commutative.

Abstract

In the paper, it is proved that a connected MAP solvable topo-logical group is commutative and that an arcwise connected MAP prosolvable pro-Lie group is commutative. Thus, the solvable radical of any arcwise con-nected MAP pro-Lie group is commutative.

참고문헌 (18)

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  3. M. Got^o, "On an arcwise connected subgroup of a Lie group", Proc. Amer. Math. Soc, 20, pp.157~162 (1969)
  4. K.H. Hofmann, "The Structure of Compact Groups" (1998), de Gruyter
  5. K. H. Hofmann, "The Lie Theory of Connected Pro Lie Groups" (2007), European Mathematical Society
  6. K. Iwasawa, "On some types of topological groups", Ann. of Math, 50, pp.507~558 (1949)
  7. 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
  8. 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.183~224 (2008)
  9. 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
  10. A. I. Shtern, "Von Neumann kernel of a connected locally compact group", revisited, Adv. Stud. Contemp. Math, 21(1), pp.313~318 (2010)
  11. Shtern, "HOMOMORPHIC IMAGES OF CONNECTED LIE GROUPS IN COMPACT GROUPS", Advanced Studies in Contemporary Mathematics, 20(1), pp.1~6 (2010), 장전수학회
  12. A. I. Shtern, "Connected Lie groups having faithful locally bounded (not necessarily continuous) nite dimensional representations", Russ. J. Math. Phys, 16(4), pp.566~567 (2009)
  13. 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
  14. A. I. Shtern, "Von Neumann kernels of connected Lie groups", revisited and re¯ned, Russ. J. Math. Phys, 17(2), pp.262~266 (2010)
  15. E. S. Thomas, "Connected subgroups of Lie groups", Illinois J. Math, 31(4), pp.689~691 (1987)
  16. J. von Neumann, "Almost periodic functions in a group", I, Trans. Amer. Math. Soc, 36, pp.445~492 (1934)
  17. A. Weil, "L'int egration dans les groupes topologiques et ses applications" (1953), Hermann
  18. H. Yamabe, "On an arcwise connected subgroup of a Lie group", Osaka Math. J, 2(1), pp.13~14 (1950)

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