Frontiers of Mathematics in China >

2021 , Vol. 16 >Issue 3: 771 - 782

DOI: https://doi.org/10.1007/s11464-021-0940-7

RESEARCH ARTICLE

Transversality on locally pseudocompact groups

  • Fucai LIN , 1,2 ,
  • Zhongbao TANG 1
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  • 1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
  • 2. Fujian Key Laboratory of Granular Computing and Applications, Minnan Normal University, Zhangzhou 363000, China

Received date: 20 Jul 2020

Accepted date: 13 May 2021

Published date: 15 Jun 2021

Copyright

2021 Higher Education Press
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Abstract

Two non-discrete Hausdorff group topologies τ and δ on a group G are called transversal if the least upper bound τ∨δ of τ and δ is the discrete topology. In this paper, we discuss the existence of transversal group topologies on locally pseudocompact, locally precompact, or locally compact groups. We prove that each locally pseudocompact, connected topological group satisfies central subgroup paradigm, which gives an affrmative answer to a problem posed by Dikranjan, Tkachenko, and Yaschenko [Topology Appl., 2006, 153:3338-3354]. For a compact normal subgroup K of a locally compact totally disconnected group G, if G admits a transversal group topology, then G/K admits a transversal group topology, which gives a partial answer again to a problem posed by Dikranjan, Tkachenko, and Yaschenko in 2006. Moreover, we characterize some classes of locally compact groups that admit transversal group topologies.

Key words： Transversal group topology; locally pseudocompact group; locally compact group; locally precompact; connected space; central topological group

Cite this article

Fucai LIN , Zhongbao TANG . Transversality on locally pseudocompact groups[J]. Frontiers of Mathematics in China, 2021 , 16(3) : 771 -782 . DOI: 10.1007/s11464-021-0940-7

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