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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.26 no.3 Antofagasta Dec. 2007

http://dx.doi.org/10.4067/S0716-09172007000300008 

 

Proyecciones Journal of Mathematics
Vol. 26, Nº 3, pp. 341-356, December 2007.
Universidad Católica del Norte
Antofagasta - Chile


ON THE LOCAL HYPERCENTER OF A GROUP


JOSÉ IVÁN SILVA RAMOS 1
RUDOLF MAIER 2

1 Universidade Federal do Acre, Brazil.
2 Universidade de Brasilia, Brazil.

Correspondencia a:



Abstract
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.


2000 Mathematics Subject Classification : 20E25, 20E28, 20F14

REFERENCES
[1] Baer, R. The hypercenter of a group ; Acta Math. 89 ; pp. 165-208         [ Links ](1953)
[2] McLain, D. H., On locally nilpotent groups; Proc. Cambridge Philos. Soc. 52 ; pp. 5-11         [ Links ](1956).
[3] Neumann, B. H. Groups covered by finitely many cosets; Publ. Math. Debrecen 3 ; pp. 227-242         [ Links ](1954).
[4] Ramos, J. I. S., Subgrupos preservadores de propriedades em grupos. Tese de Doutorado, Universidade de Brasília,         [ Links ](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,         [ Links ](2006).
[6] Robinson, D. J. S. A course in the theory of groups; Springer Verlag; New York-Berlin-Heidelberg         [ Links ](1996).
[7] Robinson, D. J. S., Finiteness Conditions and generalized soluble groups; Part 1, Springer Verlag (1972).
        [ Links ]

JOSÉ IVÁN SILVA RAMOS
Universidade Federal do Acre, Brazil
Departamento de Matemática
BR - 69.915-900 Rio Branco - AC
Brazil
e-mail : mailto:ivanr@ufac.br

RUDOLF MAIER
Universidade de Brazilia
Departamento de Matemática - IE,
BR - 70.910-900 Brasília - DF
Brazil
e-mail : mailto:maierr@mat.unb.br

Received : November 2006. Accepted : October 2007

 

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