On wreath product of permutation groups
DOI:
https://doi.org/10.4067/S0716-09172007000100004Keywords:
Centre, Faithful, Groups, Primitive, Stabiliser, Transitive, Wreath product.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.
References
[1] Audu M. S. On Transitive Permutation Groups. Africa Mathematika, Journal of African Mathematical Union. Vol. 4 (2) : pp.155 − 160,(1991).
[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).
[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).
[4] Dinneen M. J. Faver V. and Fellows M. R. Algebraic constructions of effi- cient broadcast networks, Applied Algebra, Algebraic Algorithms and errocorrecting codes, Lecture Notes in Computer SZcience, Vol. 539 Springer, Berli, (1991).
[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).
[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).
[4] Dinneen M. J. Faver V. and Fellows M. R. Algebraic constructions of effi- cient broadcast networks, Applied Algebra, Algebraic Algorithms and errocorrecting codes, Lecture Notes in Computer SZcience, Vol. 539 Springer, Berli, (1991).
Published
2017-04-18
How to Cite
[1]
I. A. A. and M. S. Audu, “On wreath product of permutation groups”, Proyecciones (Antofagasta, On line), vol. 26, no. 1, pp. 73-90, Apr. 2017.
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