M. R. Dixon, L. A. Kurdachenko, I. Ya. Subbotin, “On various rank conditions in infinite groups”, Algebra Discrete Math., 2007, no. 4, 23

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Algebra and Discrete Mathematics, 2007, Issue 4, Pages 23–44 (Mi adm232)

This article is cited in 14 scientific papers (total in 14 papers)

SURVEY ARTICLE

On various rank conditions in infinite groups

M. R. Dixon^a, L. A. Kurdachenko^b, I. Ya. Subbotin^c

^a Department of Mathematics, University of Alabama, Tuscoloosa, AL 35487–0350, U.S.A.
^b Department of Algebra, National Dnipropetrovsk University, Vul. Naukova 13. Dnipropetrovsk 50, Ukraine 49050
^c Department of Mathematics and Natural Sciuences, National University, 5245 Pacific Concourse Drive, Los Angeles, CA 90045–6904, USA

Full-text PDF (298 kB) Citations (14)

Abstract: In the current survey the authors consider some of the main theorems concerning groups satisfying certain rank con- ditions. They present these theorems starting with recently estab- lished results. This order of exposition is different, indeed opposite to chronological, but it allows them to present the main develop- ment of the theory. They illustrate the connections between the different ranks emphasizing, in particular, the connection between the special rank and the Hirsch–Zaitsev rank.

Keywords: rank, Hirsh–Zaitsev rank, special rank.

Received: 11.05.2007
Revised: 11.05.2007

Bibliographic databases:

Document Type: Article

MSC: 20E25, 20E34, 20F19

Language: English

Citation: M. R. Dixon, L. A. Kurdachenko, I. Ya. Subbotin, “On various rank conditions in infinite groups”, Algebra Discrete Math., 2007, no. 4, 23–44

Citation in format AMSBIB

\Bibitem{DixKurSub07}

\by M.~R.~Dixon, L.~A.~Kurdachenko, I.~Ya.~Subbotin

\paper On various rank conditions in infinite groups

\jour Algebra Discrete Math.

\yr 2007

\issue 4

\pages 23--44

\mathnet{http://mi.mathnet.ru/adm232}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2423708}

\zmath{https://zbmath.org/?q=an:1164.20009}

Linking options:

https://www.mathnet.ru/eng/adm232

https://www.mathnet.ru/eng/adm/y2007/i4/p23

This publication is cited in the following 14 articles:

Velychko T.V., “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
Tumanova E.A., “on the Residual Properties of Generalized Direct Products of Groups”, Lobachevskii J. Math., 41:9, SI (2020), 1704–1711
Sokolov E.V., Tumanova E.A., “to the Question of the Root-Class Residuality of Free Constructions of Groups”, Lobachevskii J. Math., 41:2, SI (2020), 260–272
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
E. A. Tumanova, “On the root-class residuality of certain HNN-extensions of groups”, Russian Math. (Iz. VUZ), 64:12 (2020), 38–45
E. V. Sokolov, “Separability of the subgroups of residually nilpotent groups in the class of finite $\pi$-groups”, Siberian Math. J., 58:1 (2017), 169–175
Pypka A.A., “Relationships Between the Factors of the Central Series and the Nilpotent Residual in Some Infinite Groups”, Adv. Group Theory Appl., 4 (2017), 65–82
N. N. Semko, T. V. Velychko, “On groups whose subgroups of infinite special rank are transitively normal”, Algebra Discrete Math., 24:1 (2017), 34–45
E. V. Sokolov, E. A. Tumanova, “Sufficient conditions for the root-class residuality of certain generalized free products”, Siberian Math. J., 57:1 (2016), 135–144
Martyn R. Dixon, Leonid A. Kurdachenko, Aleksandr A. Pypka, Igor Ya. Subbotin, “Groups satisfying certain rank conditions”, Algebra Discrete Math., 22:2 (2016), 184–200
E. A. Tumanova, “On the root-class residuality of generalized free products with a normal amalgamation”, Russian Math. (Iz. VUZ), 59:10 (2015), 23–37
E. A. Tumanova, “Ob approksimiruemosti kornevymi klassami HNN-rasshirenii grupp”, Model. i analiz inform. sistem, 21:4 (2014), 148–180
Kurdachenko L.A., Munoz-Escolano J.M., Otal J., “Groups in Which the Normal Closures of Cyclic Subgroups Have Finite Section Rank”, Int. J. Algebr. Comput., 22:4 (2012), 1250032
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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