Abstract:
All considered groups are finite. Let $G$ be a group. Then $c_{\infty}^\omega\mathrm{form}(G)$ denotes the intersection of all totally $\omega$-composition formations containing $G$. The formation $c_{\infty}^\omega\mathrm{form}(G)$ is called a totally $\omega$-composition formation generated by $G$ or a one-generated totally $\omega$-composition formation. A totally $\omega$-composition formation $\mathfrak{F}$ is called a bounded, if $\mathfrak{F}$ is a subformation of some one-generated totally $\omega$-composition formation, that is, $\mathfrak{F}\subseteq c_{\infty}^\omega\mathrm{form}(G)$ for some group $G$. In this paper, criteria for the one-generation (boundedness) of a totally $\omega$-composition formation are obtained.
Citation:
I. P. Los, V. G. Safonov, “On one-generated and bounded totally $\omega$-composition formations of finite groups”, PFMT, 2021, no. 4(49), 101–107
\Bibitem{LosSaf21}
\by I.~P.~Los, V.~G.~Safonov
\paper On one-generated and bounded totally $\omega$-composition formations of finite groups
\jour PFMT
\yr 2021
\issue 4(49)
\pages 101--107
\mathnet{http://mi.mathnet.ru/pfmt818}
\crossref{https://doi.org/10.54341/20778708_2021_4_49_101}
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https://www.mathnet.ru/eng/pfmt818
https://www.mathnet.ru/eng/pfmt/y2021/i4/p101
This publication is cited in the following 2 articles:
I. P. Los, V. G. Safonov, “On the properties of the lattice of τ-closed totally ω-composition formations”, Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk, 60:3 (2024), 183
I. P. Los, V. G. Safonov, “Otdelimost reshetki $\tau$-zamknutykh totalno $\omega$-kompozitsionnykh formatsii konechnykh grupp”, Tr. In-ta matem., 31:2 (2023), 44–56
Citation in format AMSBIB
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