On the local hypercenter of a group


  • José Iván Silva Ramos Universidade Federal do Acre.
  • Rudolf Maier Universidade de Brasilia.




We introduce a local hypercenter of an arbitrary group and study its basic properties. With this concept, it turns out that classical theorems of Baer, Mal’cev and McLain on locally nilpotent groups can be obtained as special cases of statements which are valid in any group. Furthermore, we investigate the connection between the local hypercenter of a group and the intersection of its maximal locally nilpotent subgroups.

Author Biographies

José Iván Silva Ramos, Universidade Federal do Acre.

Departamento de Matemática.

Rudolf Maier, Universidade de Brasilia.

Departamento de Matemática.


[1] Baer, R. The hypercenter of a group ; Acta Math. 89 ; pp. 165-208 (1953)

[2] McLain, D. H., On locally nilpotent groups; Proc. Cambridge Philos. Soc. 52 ; pp. 5-11 (1956).

[3] Neumann, B. H. Groups covered by finitely many cosets; Publ. Math. Debrecen 3 ; pp. 227-242 (1954).

[4] Ramos, J. I. S., Subgrupos preservadores de propriedades em grupos. Tese de Doutorado, Universidade de Brasília, (2003).

[5] Ramos, J. I. S. and Maier, R. Property preserving subgroups of a group. JP Journal of Algebra, Number Theory and Applications 6, Issue 2, pp. 237-264, (2006).

[6] Robinson, D. J. S. A course in the theory of groups; Springer Verlag; New York-Berlin-Heidelberg (1996).

[7] Robinson, D. J. S., Finiteness Conditions and generalized soluble groups; Part 1, Springer Verlag (1972).



How to Cite

J. I. Silva Ramos and R. Maier, “On the local hypercenter of a group”, Proyecciones (Antofagasta, On line), vol. 26, no. 3, pp. 341-356, Apr. 2017.




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