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Algebra Discrete Math., 2012, Volume 13, Issue 2, Pages 169–208 (Mi adm73)  

SURVEY ARTICLE

S. N. Chernikov and the development of infinite group theory

M. R. Dixona, V. V. Kirichenkob, L. A. Kurdachenkoc, J. Otald, N. N. Semkoe, L. A. Shemetkovf, I. Ya. Subboting

a Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350 USA
b Department of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska, 64, Kyiv, 01033, Ukraine
c Department of Algebra and Geometry, School of Mathematics and Mechanics, National University of Dnepropetrovsk, Gagarin prospect 72, Dnepropetrovsk 10, 49010, Ukraine
d Department of Mathemathics-IUMA, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
e Department of Mathematics, National State Tax Service Academy of Ukraine, 09200 Irpen, Ukraine
f Department of Algebra and Geometry, Gomel Francisk Skorina State University, Gomel 246019, Belarus
g Department of Mathematics and Natural Sciences, College of Letters and Sciences, National University, 5245 Pacific Concourse Drive, Los Angeles, CA 90045-6904, USA

Abstract: In this survey, the authors want to show the development and continuation of some studies, in which S. N. Chernikov stood as the main originator and to demonstrate clearly the extent of influence exerted by the ideas and results of S. N. Chernikov on the modern theory of infinite groups.

Keywords: infinite groups, finiteness conditions, generalized soluble groups, generalized nilpotent groups, Chernikov groups, FC–groups, CC–groups.

Full text: PDF file (346 kB)
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Bibliographic databases:
MSC: 20-00, 20B07, 20C07, 20E15, 20E07, 20E25, 20E26, 20E28, 20E34, 20E36, 20E45, 20F14, 20F16, 20F18, 20F19, 20F22, 20F24, 20F50
Received: 27.02.2012
Accepted:27.02.2012
Language:

Citation: M. R. Dixon, V. V. Kirichenko, L. A. Kurdachenko, J. Otal, N. N. Semko, L. A. Shemetkov, I. Ya. Subbotin, “S. N. Chernikov and the development of infinite group theory”, Algebra Discrete Math., 13:2 (2012), 169–208

Citation in format AMSBIB
\Bibitem{DixKirKur12}
\by M.~R.~Dixon, V.~V.~Kirichenko, L.~A.~Kurdachenko, J.~Otal, N.~N.~Semko, L.~A.~Shemetkov, I.~Ya.~Subbotin
\paper S.\,N.~Chernikov and the development of infinite group theory
\jour Algebra Discrete Math.
\yr 2012
\vol 13
\issue 2
\pages 169--208
\mathnet{http://mi.mathnet.ru/adm73}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3027506}
\zmath{https://zbmath.org/?q=an:06120570}


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