Abstract:
This paper devoted to the non-periodic locally generalized radical groups, whose subgroups of infinite special rank are transitively normal. We proved that if such a group GG includes an ascendant locally nilpotent subgroup of infinite special rank, then GG is abelian.
Keywords:
finite special rank, soluble group, periodic group, locally nilpotent radical, locally nilpotent residual, transitively normal subgroups.
Citation:
L. A. Kurdachenko, I. Ya. Subbotin, T. V. Velychko, “On the non-periodic groups, whose subgroups of infinite special rank are transitively normal”, Algebra Discrete Math., 29:1 (2020), 74–84
\Bibitem{KurSubVel20}
\by L.~A.~Kurdachenko, I.~Ya.~Subbotin, T.~V.~Velychko
\paper On the non-periodic groups, whose subgroups of~infinite special rank are transitively normal
\jour Algebra Discrete Math.
\yr 2020
\vol 29
\issue 1
\pages 74--84
\mathnet{http://mi.mathnet.ru/adm740}
\crossref{https://doi.org/10.12958/adm1357}
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Linking options:
https://www.mathnet.ru/eng/adm740
https://www.mathnet.ru/eng/adm/v29/i1/p74
This publication is cited in the following 2 articles:
T. V. Velychko, “On the structure of some non-periodic groups whose subgroups of infinite special rank are transitively normal”, Carpathian Math. Publ., 13:2 (2021), 515–521
T.V. Velychko, “On the structure of some non-periodic groups whose subgroups of infinite special rank are transitively normal”, Dopov. Nac. akad. nauk Ukr., 2021, no. 6, 12
Citation in format AMSBIB
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