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The twisted commutator subgroups and questions of Fel’shtyn and Troitsky

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Abstract

In this paper, we study the notion of the twisted conjugacy separability developed in Fel’shtyn and Troitsky (J K-Theory 1:1–40, 2008). We give an example of group with twisted conjugacy separability, but without residual finiteness. Thus, we find the negative answers on the several open questions formulated by Fel’shtyn and Troitsky (Topol Appl 157:1724–1735, 2010). In addition, we discuss the generalization of usual the commutator subgroup, especially for some relations among Nielsen fixed point theory and the twisted commutator subgroup.

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References

  1. Fel’shtyn, A.: New directions in Nielsen-Reidemeister theory. Top. Appl. 157, 1724–1735 (2010)

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Acknowledgements

It is a pleasure to record here our gratitude to Prof. Fel!‘Çshtyn and Prof. Troitsky for a major influence on the direction of our recent research into topological fixed point theory. Especially, the authors would like to thank Prof. Xuezhi Zhao for helpful discussions, suggestions, and advice about this paper. We also would like to thank the referee for his/her careful readings and many suggestions that improved substantially the presentation of this work.

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  1. Department of Mathematics, University of Science, Unjong District, Pyongyang, Democratic People’s Republic of Korea

    Taewon Ryu, Songho Li & Cholyong Kang

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  1. Taewon Ryu
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  2. Songho Li
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  3. Cholyong Kang
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Correspondence to Taewon Ryu.

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Ryu, T., Li, S. & Kang, C. The twisted commutator subgroups and questions of Fel’shtyn and Troitsky. J. Fixed Point Theory Appl. 22, 80 (2020). https://doi.org/10.1007/s11784-020-00811-7

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  • DOI: https://doi.org/10.1007/s11784-020-00811-7

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