On the Wreath Product of Group by Some Other Groups
In this paper, we will generate the wreath product
11 12 M wrM using only two permutations. Also, we will show the
structure of some groups containing the wreath product 11 12 M wrM .
The structure of the groups founded is determined in terms of wreath
product k (M wrM ) wrC 11 12 . Some related cases are also included.
Also, we will show that 132K+1 S and 132K+1 A can be generated
using the wreath product k (M wrM ) wrC 11 12 and a transposition in
132K+1 S and an element of order 3 in 132K+1 A . We will also show
that 132K+1 S and 132K+1 A can be generated using the wreath
product 11 12 M wrM and an element of order k +1.
[1] A. M. Hammas and I. R. Al-Amri, Symmetric generating set of the
alternating groups , JKAU: Educ. Sci., 7 (1994), 3-7.
[2] B. H. Shafee, Symmetric generating set of the groups and using th the
wreath product , Far East Journal of Math. Sci. (FJMS), 28(3) (2008),
707-711.
[3] B. H. Shafee and I. R. Al-Amri, On the Structure of Some Groups
Containing , International Journal of Algebra, vol.6, 2012,no.17, 857-
862.
[4] I.R. Al-Amri, Computational methods in permutation groups , ph.D
Thesis, University of St. Andrews, September 1992.
[5] I.R. Al-Amri, and A.M. Hammas, Symmetric generating set of Groups
and , JKAU: Sci., 7 (1995), 111-115.
[6] J. H. Conway and others, Atlas of Finite Groups, Oxford Univ. Press,
New York, 1985.
[1] A. M. Hammas and I. R. Al-Amri, Symmetric generating set of the
alternating groups , JKAU: Educ. Sci., 7 (1994), 3-7.
[2] B. H. Shafee, Symmetric generating set of the groups and using th the
wreath product , Far East Journal of Math. Sci. (FJMS), 28(3) (2008),
707-711.
[3] B. H. Shafee and I. R. Al-Amri, On the Structure of Some Groups
Containing , International Journal of Algebra, vol.6, 2012,no.17, 857-
862.
[4] I.R. Al-Amri, Computational methods in permutation groups , ph.D
Thesis, University of St. Andrews, September 1992.
[5] I.R. Al-Amri, and A.M. Hammas, Symmetric generating set of Groups
and , JKAU: Sci., 7 (1995), 111-115.
[6] J. H. Conway and others, Atlas of Finite Groups, Oxford Univ. Press,
New York, 1985.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:56751", author = "Basmah H. Shafee", title = "On the Wreath Product of Group by Some Other Groups", abstract = "In this paper, we will generate the wreath product
11 12 M wrM using only two permutations. Also, we will show the
structure of some groups containing the wreath product 11 12 M wrM .
The structure of the groups founded is determined in terms of wreath
product k (M wrM ) wrC 11 12 . Some related cases are also included.
Also, we will show that 132K+1 S and 132K+1 A can be generated
using the wreath product k (M wrM ) wrC 11 12 and a transposition in
132K+1 S and an element of order 3 in 132K+1 A . We will also show
that 132K+1 S and 132K+1 A can be generated using the wreath
product 11 12 M wrM and an element of order k +1.", keywords = "Group presentation, group generated by n-cycle,
Wreath product, Mathieu group.", volume = "7", number = "3", pages = "354-3", }