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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.26 n.1 Antofagasta mayo 2007

http://dx.doi.org/10.4067/S0716-09172007000100004 

Proyecciones Journal of Mathematics
Vol. 26, No 1, pp. 73-90, May 2007.
Universidad Católica del Norte
Antofagasta - Chile



ON WREATH PRODUCT OF PERMUTATION GROUPS


IBRAHIM A. A. USMANU DANFODIYO UNIVERSITY, SOKOTO - NIGERIA
AUDU M. S.UNIVERSITY OF JOS, JOS - NIGERIA


Correspondencia a:



Abstract
This report is essentially an upgrade of the results of Audu (see [1] and [2]) on some finite permutation groups. It consists of the basic procedure for computing wreath product of groups. We also discussed the conditions under which the wreath products of permutation groups are faithful, transitive and primitive. Further, the centre of the stabilizer and the centre of wreath products was investigated, and finally, an illustration was supplied to support our findings.

Keywords: Centre, Faithful, Groups, primitive, Stabiliser, Transitive, Wreath product.

REFERENCES
[1] Audu M. S. On Transitive Permutation Groups. Africa Mathematika, Journal of African Mathematical Union. Vol. 4 (2) : pp.155 — 160,(1991).         [ Links ]
[2] Audu M. S. Wreath Product of Permutation Groups. A Research Oriented Course In Arithmetics of Elliptic Curves, Groups and Loops, Lecture Notes Series, National Mathematical Centre, Abuja, (2001).         [ Links ]
[3] Praeger C. E. and Scheider C. Ordered Triple Designs And Wreath Product of Groups technical report supported by an Australian Research Council large grant, (2002).         [ Links ]
[4] Dinneen M. J. Faver V. and Fellows M. R. Algebraic constructions of efficient broadcast networks, Applied Algebra, Algebraic Algorithms and erro-correcting codes, Lecture Notes in Computer SZcience, Vol. 539 Springer, Berli, (1991).
        [ Links ]

Ibrahim A. A.
Mathematics Department
Usmanu Danfodiyo University
PMB 2346 Sokoto
Nigeria
e-mail : aminualhaji@yahoo.co.uk

Audu M. S.
Mathematics Department
University of Jos
PMB 2084 JOS
PLATEAU STATE
NIGERIA 930003
e-mail : aminualhaji@yahoo.co.uk

Received : November 2006. Accepted : March 2007