On the structure of groups, whose subgroups are either normal or core-free

Authors

  • L.A. Kurdachenko Oles Honchar Dnipro National University, Ukraine
  • A.A. Pypka Oles Honchar Dnipro National University, Ukraine
  • I.Ya. Subbotin National University, Los Angeles, USA

DOI:

https://doi.org/10.15407/dopovidi2019.04.017

Keywords:

core-free subgroup, Dedekind group, normal subgroup

Abstract

We investigate the influence of some natural types of subgroups on the structure of groups. A subgroup H of the group G is called core-free if CoreG(H) = 〈1〉. We study the groups, in which every subgroup is either normal or core-free. More precisely, we obtain the structures of monolithic and non-monolithic groups with this property.

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References

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Kurdachenko, L.A., Pypka, A.A. & Semko, N.N. (2016). The groups whose cyclic subgroups are either ascendant or almost self-normalizing. Algebra Discrete Math., 21, No. 1, pp. 111-127.

Zhao, L., Li, Y. & Gong, L. (2018). Finite groups in which the cores of every non-normal subgroups are trivial. Publ. Math. Debrecen, 93, No. 3-4, pp. 511-516. doi: https://doi.org/10.5486/PMD.2018.8288

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Published

21.04.2024

How to Cite

Kurdachenko, L., Pypka, A., & Subbotin, I. (2024). On the structure of groups, whose subgroups are either normal or core-free . Reports of the National Academy of Sciences of Ukraine, (4), 17–20. https://doi.org/10.15407/dopovidi2019.04.017

Issue

No. 4 (2019): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

License

Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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