On some types of propermutable subgroups and their generalizations in finite groups

Authors

  • A.A. Pypka Oles Honchar Dnipro National University
  • D.Yu. Storozhenko Oles Honchar Dnipro National University

DOI:

https://doi.org/10.15407/dopovidi2017.07.018

Keywords:

finite group, propermutable subgroup, S-propermutable subgroup

Abstract

We found some specific examples of propermutable and S-propermutable subgroups in finite groups. In particular, we have given the positive answer to the question 18.91 (a) from the Kourovka Notebook.

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References

Dedekind, R. (1897). Ueber Gruppen, deren sämmtliche Theiler Normaltheiler sind. Math. Ann., 48, № 4, pp. 548-561. https://doi.org/10.1007/BF01447922

Ore, O. (1939). Contributions in the theory of groups of finite order. Duke Math. J., 5, No. 2, pp. 431-460. https://doi.org/10.1215/S0012-7094-39-00537-5

Yi, X., Skiba, A. N. (2015). On S-propermutable subgroups of finite groups. Bull. Malays. Math. Sci. Soc., 38, No. 2, pp. 605–616. https://doi.org/10.1007/s40840-014-0038-4

Mazurov, V. D., Khukhro, E. I. (Eds.) (2014). The Kourovka Notebook: Unsolved Problems in Group Theory (18th ed.). Novosibirsk: Sobolev Inst. Math.

Yi, X., Skiba, A. N. (2014). Some new characterizations of PST-groups. J. Algebra, 399, pp. 39–54. https://doi.org/10.1016/j.jalgebra.2013.10.001

Published

15.09.2024

How to Cite

Pypka, A., & Storozhenko, D. (2024). On some types of propermutable subgroups and their generalizations in finite groups . Reports of the National Academy of Sciences of Ukraine, (7), 18–20. https://doi.org/10.15407/dopovidi2017.07.018

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