Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

IMPACT FACTOR 2018: 0.726
5-year IMPACT FACTOR: 0.869

CiteScore 2018: 0.90

SCImago Journal Rank (SJR) 2018: 0.323
Source Normalized Impact per Paper (SNIP) 2018: 0.821

Mathematical Citation Quotient (MCQ) 2018: 0.34

ICV 2017: 161.82

Open Access
See all formats and pricing
More options …
Volume 11, Issue 10


Volume 13 (2015)

The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group

Leonid Kurdachenko / Javier Otal
Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0284-y


We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.

MSC: 20F14; 20F19; 20F99

Keywords: Upper central series; Lower central series; Schur theorem; Baer theorem; Finite special rank; Generalized radical group; Hypercentral group

  • [1] Adian S.I., Certain torsion-free groups, Izv. Akad. Nauk SSSR Ser. Mat., 1971, 35, 459–468 (in Russian) Google Scholar

  • [2] Baer R., Endlichkeitskriterien für Kommutatorgruppen, Math. Ann., 1952, 124, 161–177 http://dx.doi.org/10.1007/BF01343558CrossrefGoogle Scholar

  • [3] Franciosi S., de Giovanni F., Kurdachenko L.A., The Schur property and groups with uniform conjugacy classes, J. Algebra, 1995, 174(3), 823–847 http://dx.doi.org/10.1006/jabr.1995.1155CrossrefGoogle Scholar

  • [4] Kaloujnine L.A., Über gewisse Beziehungen zwischen eine Gruppe und ihren Automorphismen, In: Bericht über die Mathematiker-Tagung, Berlin, January 1953, Deutscher Verlag der Wissenschaften, Berlin, 1953, 164–172 Google Scholar

  • [5] Kurdachenko L.A., Artinian Modules over Group Rings, In: Infinite Groups and Related Algebraic Structures, Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1993, 160–177 (in Russian) Google Scholar

  • [6] Kurdachenko L.A., Otal J., Subbotin I.Ya., Artinian Modules over Group Rings, Front. Math., Birkhäuser, Basel, 2007 Google Scholar

  • [7] Kurdachenko L.A., Shumyatsky P., The ranks of central factor and commutator groups, Math. Proc. Cambridge Phil. Soc., 2013, 154(1), 63–69 http://dx.doi.org/10.1017/S0305004112000412CrossrefGoogle Scholar

  • [8] Lubotzky A., Mann A., Powerful p-groups. I. Finite groups, J. Algebra, 1987, 105(2), 484–505 http://dx.doi.org/10.1016/0021-8693(87)90211-0CrossrefGoogle Scholar

  • [9] Makarenko N.Yu., Rank analogues of Hall’s and Baer’s theorems, Siberian Math. J., 2000, 41(6), 1137–1140 http://dx.doi.org/10.1023/A:1004828422007CrossrefGoogle Scholar

  • [10] Schur J., Über die Darstellungen der endlichen Gruppen durch gebrochene lineare substitutionen, J. Reine Angew. Math., 1904, 127, 20–50 Google Scholar

  • [11] Wiegold J., Groups with boundedly finite classes of conjugate elements, Proc. Roy. Soc. London Ser. A, 1956, 238(1214), 389–401 Google Scholar

  • [12] Wiegold J., Multiplicators and groups with finite central factor-groups, Math. Z., 1965, 89(4), 345–347 http://dx.doi.org/10.1007/BF01112166CrossrefGoogle Scholar

About the article

Published Online: 2013-07-20

Published in Print: 2013-10-01

Citation Information: Open Mathematics, Volume 11, Issue 10, Pages 1732–1741, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0284-y.

Export Citation

© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Leonid A. Kurdachenko, Javier Otal, and Alexander A. Pypka
Journal of Algebra and Its Applications, 2015, Volume 14, Number 05, Page 1550075

Comments (0)

Please log in or register to comment.
Log in