An infinite family of finite 2-groups with fixed co-class

Document Type : Research Paper

Authors

1 Department of Mathematics and Applications, Faculty of Science, University of Mohaghegh Ardabili, P. O. Box 56199-11367, Ardabil, Iran.

2 Department of Mathematics and Applications, Faculty of Science, University of Mohaghegh Ardabili, P. O. Box 56199-11367, Ardabil, Iran

Abstract

In [1] six pro-2-groups of finite and fixed coclasses is studied. Infinite sequences of finite 2-groups arising from this pro2-groups also investigated. One of the five infinite sequences associated with the pro-2-group S = ha, u | a 2 = u 4 ,(u 2 ) a = u −2 i is the sequence Gj (1, 2) = ha, u | a 2 u −4 (u −1 a) 2 j ,(u 2 ) a u 2 (u −1 a) 2 j+1 ,(u −1 a) 2 j+2 i. In this paper we calculate the orders of the members of this infinite family

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References

[1] H. Abdolzadeh and B. Eick, On Effcient Presentations for Infinite Sequences of 2-Groups with Fixed Coclass, Algebra Colloquium 20(4) (2013), 561-572.
[2] A. Arjomandfar and H. Doostie, Proving the efficiency of pro-2-groups of fixed co-classes, Bull. Iranian Math. Soc. 37 (2011), 73-80.
[3] M. J. Beetham and C. M. Campbell, A note on the Todd-Coxeter coset enumer-ation algorithm, Proc. Edinburgh Math. Soc. 20(2) (1976), 73-79.
[4] H. Doostie and M. Hashemi. Fibonacci lengths involving the Wall number K(n),Journal of Applied Mathematics and Computing 20(1-2) (2006), 171-180.
[5] D. L. Johnson, Presentations of Groups,London Math. Soc. stud. texts. Cambridge University Press,Cambridge 15(1990)
Journal of Hyperstructures
Volume 6, Issue 2
December 2017
Pages 96-101

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