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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 3, Pages 234–239 (Mi timm596)  

This article is cited in 3 scientific papers (total in 3 papers)

On Shunkov groups with a strongly embedded almost layer-finite subgroup

V. I. Senashov

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences

Abstract: Infinite Shunkov groups with the following condition are studied: the normalizer of any finite nontrivial subgroup has an almost layer-finite periodic part. Under this condition, the almost layer-finiteness of the periodic part of a Shunkov group with a strongly embedded almost layer-finite subgroup is established. Earlier, the author proved the almost layer-finiteness of a Shunkov group with a strongly embedded subgroup either under the condition that all proper subgroups are almost layer-finite or under the condition that the group is periodic. The case of a strongly embedded subgroup with a Chernikov almost layer-finite periodic part was also investigated earlier.

Keywords: infinite groups, finiteness conditions, layer-finiteness, periodicity.

Full text: PDF file (135 kB)
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UDC: 512.54
Received: 10.11.2009

Citation: V. I. Senashov, “On Shunkov groups with a strongly embedded almost layer-finite subgroup”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 3, 2010, 234–239

Citation in format AMSBIB
\Bibitem{Sen10}
\by V.~I.~Senashov
\paper On Shunkov groups with a~strongly embedded almost layer-finite subgroup
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 3
\pages 234--239
\mathnet{http://mi.mathnet.ru/timm596}
\elib{https://elibrary.ru/item.asp?id=15173484}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Senashov, “On Groups with a Strongly Imbedded Subgroup Having an Almost Layer-Finite Periodic Part”, Ukr. Math. J., 64:3 (2012), 433–440  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. I. Senashov, “On Sylow Subgroups of Some Shunkov Groups”, Ukr. Math. J., 67:3 (2015), 455–463  crossref  mathscinet  zmath  isi  elib  scopus
    3. V. I. Senashov, “Characterizations of the Groups With Almost Layer-Finite Periodic Parts”, Ukr. Math. J., 69:7 (2017), 1123–1131  crossref  mathscinet  isi  scopus
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