On the groups, whose all subgroups with infinite special rank are transitively normal

Authors

  • N.N. Semko University of State Fiscal Service of Ukraine, Irpin
  • T.V. Velichko Oles Honchar Dnipro National University

DOI:

https://doi.org/10.15407/dopovidi2017.08.017

Keywords:

finite special rank, locally nilpotent radical, locally nilpotent residual, periodic group, soluble group, transitively normal subgroups

Abstract

The periodic soluble groups, whose subgroups with infinite special rank are transitively normal, and the struc ture of a periodic radical group, whose subgroups with infinite special rank are transitively normal, are described.

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References

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Dixon, M. R., Kurdachenko, L. A., Pypka, A. A. & Subbotin, I. Ya. (2016). Groups satisfying certain rank conditions. Algebra Discrete Math., 4, pp. 23-44.

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Baer, R. (1933). Situation der Untergruppen und Struktur der Gruppe. S.-B. Heidelberg Akad., 2, pp. 12-17.

Published

15.09.2024

How to Cite

Semko, N., & Velichko, T. (2024). On the groups, whose all subgroups with infinite special rank are transitively normal . Reports of the National Academy of Sciences of Ukraine, (8), 17–19. https://doi.org/10.15407/dopovidi2017.08.017