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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 414, Pages 31–39 (Mi znsl5666)  
This article is cited in 3 scientific papers (total in 3 papers)

Infinite groups with rank restrictions on subgroups

F. de Giovanni

Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, I-80126 Napoli (Italy)
Full-text PDF (170 kB) Citations (3)
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Abstract: Classical results by Mal'cev and Šunkov show that locally nilpotent groups and locally finite groups of infinite rank must contain some abelian subgroups of infinite rank. In recent years, many authors have studied groups in which all subgroups of infinite rank have a given property (which can be either absolute or of embedding type). Results from these researches and some new contributions to this topic are described in this paper.
Key words and phrases: rank, locally soluble group, absolute property, embedding property.
Received: 22.09.2012
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 199, Issue 3, Pages 261–265
DOI: https://doi.org/10.1007/s10958-014-1854-7
Bibliographic databases:
Document Type: Article
UDC: 512.544
Language: English
Citation: F. de Giovanni, “Infinite groups with rank restrictions on subgroups”, Problems in the theory of representations of algebras and groups. Part 25, Zap. Nauchn. Sem. POMI, 414, POMI, St. Petersburg, 2013, 31–39; J. Math. Sci. (N. Y.), 199:3 (2014), 261–265
Citation in format AMSBIB
\Bibitem{De 13}
\by F.~de Giovanni
\paper Infinite groups with rank restrictions on subgroups
\inbook Problems in the theory of representations of algebras and groups. Part~25
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 414
\pages 31--39
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5666}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 199
\issue 3
\pages 261--265
\crossref{https://doi.org/10.1007/s10958-014-1854-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902315542}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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