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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 6, pp 1651–1658 | Cite as

On Weakly (Noncommutatively) Slender Groups

  • Hamid TorabiEmail author
  • Ali Parsa
Original Paper
  • 27 Downloads

Abstract

The class of slender groups is closed under direct sums, but it is not closed under direct product. Also, the class of noncommutatively slender groups is closed under weak direct products, but it is not closed under direct product. In this paper, we generalize the class of (noncommutatively) slender groups to weakly (noncommutatively) slender groups, which is closed under direct products and inverse limits. Also, we show that for a topological space X with first countability at \(x_0\), if \(\pi _1 (X,x_0)\) is (weakly) noncommutatively slender, then X is semilocally simply connected (homotopically Hausdorff) at \(x_0\).

Keywords

Slender groups Noncommutatively slender groups Fundamental groups 

Mathematics Subject Classification

57M07 55Q52 

Notes

Acknowledgements

The authors would like to thank the referee for the valuable comments and suggestions which have improved the manuscript and made it more readable.

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.Department of Pure MathematicsFerdowsi University of MashhadMashhadIslamic Republic of Iran

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