Advanced search
Publication Cover
Communications in Algebra Volume 47, 2019 - Issue 2
Submit an article Journal homepage
76
Views
0
CrossRef citations to date
0
Altmetric
Original Article

Groups whose factor group modulo the upper hypercenter is of finite 0-rank

Martyn R. DixonDepartment of Mathematics, University of Alabama, Tuscaloosa, Alabama, USA; Correspondence[email protected]
,
Leonid A. KurdachenkoDepartment of Algebra, Faculty of Mathematic and Mechanics, National University of Dnepropetrovsk, Dnepropetrovsk, Ukraine;
&
Igor Ya. SubbotinDepartment of Mathematics and Natural Sciences, National University, Los Angeles, California, USA
Pages 553-559 | Received 13 Apr 2018, Accepted 12 May 2018, Published online: 09 Jan 2019

References

  • Baer, R. (1951). Endlichkeitskriterien für kommutatorgruppen. Math. Ann. 124(1):161–177.
  • Baer, R. (1956). Noethersche gruppen. Math. Z. 66(1):269–288.
  • Ballester-Bolinches, A., Camp-Mora, S., Kurdachenko, L. A., Otal, J. (2013). Extension of a schur theorem to groups with a central factor with a bounded section rank. J. Algebra. 393:1–15.
  • Dixon, M. R., Kurdachenko, L. A., Otal, J. (2015). On groups whose factor-group modulo the hypercentre has finite section p-rank. J. Algebra. 440:489–503.
  • Dixon, M. R., Kurdachenko, L. A., Polyakov, N. V. (2007). Locally generalized radical groups satisfying certain rank conditions. Ricerche Mat. 56(1):43–59.
  • Dixon, M. R., Kurdachenko, L. A., Subbotin, I. Y. (2017). Ranks of Groups: The Tools, Characteristics, and Restrictions. Hoboken, NJ: John Wiley & Sons, Inc, pp. xi+309.
  • Dixon, M. R., Kurdachenko, L. A., Subbotin, I. Y. (2018). On the relationships between the factors of the upper and lower Central series in some non-periodic groups. Int. J. Group Theory. 7(1):37–50.
  • De Falco, M., de Giovanni, F., Musella, C., Sysak, Y. P. (2011). On the upper central series of infinite groups. Proc. Amer. Math. Soc. 139(2):385–389.
  • Franciosi, S., De Giovanni, F., Kurdachenko, L. A. (1995). On groups with many almost normal subgroups. Annali Di Matematica Pura Ed Applicata. 169(1):35–65.
  • Kurdachenko, L. A. (1993). Groups with minimax classes of conjugate elements. Infinite groups and related algebraic structures (Russian), Akad. Nauk Ukrainy, Inst. Mat., Kiev. pp. 160–177.
  • Kurdachenko, L. A., Otal, J. (2013). The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group. Cent. Eur. J. Math. 11(10):1732–1741.
  • Kurdachenko, L. A., Otal, J. (2015). Groups with Chernikov factor-group by hypercentral. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM. 109(2):569–579.
  • Kurdachenko, L. A., Otal, J., Subbotin, I. Y. (2010). Some criteria for existence of supplements to normal subgroups and their applications. Int. J. Algebra Comput. 20(5):689–719.
  • Kurdachenko, L. A., Otal, J., Subbotin, I. Y. (2013). On a generalization of Baer theorem. Proc. Amer. Math. Soc. 141(8):2597–2602.
  • Kurdachenko, L. A., Pypka, A. A., Semko, N. N. (2014). On some relationships between the upper and lower central series in finite groups. In: Francisk Scorina Gomel State University Proceedings 3. pp. 66–71.
  • Kurdachenko, L. A., Shumyatsky, P. (2013). The ranks of central factor and commutator groups. Math. Proc. Camb. Phil. Soc. 154(01):63–69.
  • Kurdachenko, L. A., Subbotin, I. Y. (2016). A brief history of an important classical theorem. Adv. Group Theory Appl. 2:121–124.
  • Kurosh, A. G. (1960). The Theory of Groups. New York: Chelsea Publishing Co. Translated from the Russian and edited by K. A. Hirsch. 2nd English ed. 2 volumes.
  • Kurosh, A. G. (1967). The Theory of Groups, augmented ed., Izdat. “Nauka”, Moscow.
  • Maltsev, A. I. (1948). On groups of finite rank. Mat. Sbornik. 22:351–352.
  • Neumann, B. H. (1951). Groups with finite classes of conjugate elements. Proc. London Math. Soc. s3-1(1):178–187.
  • Robinson, D. J. S. (1996). A Course in the Theory of Groups, Graduate Texts in Mathematics, Vol. 80. Berlin, Heidelberg, New York: Springer Verlag.
  • Sesekin, N. F. (1953). On locally nilpotent groups without torsion. Mat. Sbornik N.S. 32(74):407–442.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.