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Vol.2 , No. 6, Publication Date: Nov. 25, 2017, Page: 63-67
| [1] | Faisal Hussain Nesayef, Department of Mathematics, Faculty of Science, University of Kirkuk, Kirkuk, Iraq. |
The concept of length functions on groups was first introduced by Lyndon [1]. This was used to give direct proofs of many other results in combinatorial group theory. Further work was done by many others such as, Chiswell [2], [3], Hoare [4], [5], Wilkins [6], etc. The aim of the paper is to investigate the nature of some particular elements of the Quasi-HNN groups, namely the Archimedean elements N and M which are introduced in chapter two. Length functions are used to prove the connection between the elements of the Quasi-HNN group and to achieve certain objectives, such as M is a subset of N and identify the conjugates of each set.
Keywords
Archimedean Elements, Associated Subgroups, Conjugate Elements, Coset Representative, Normal Form, Quasi HNN Extension, Reduced Word
Reference
| [01] | Lyndon, R. C.; Length Function in Groups, Math. Scand, 12, 1963, 209-234. |
| [02] | Chiswell, I. M.; Abstract Length Function in groups, Math. Proc. Camb. PhilSoc., 80, 1976, 451-463. |
| [03] | Chiswell, I. M.; Length Function and Free products with amalgamation of groups´, Math. Proc. Camb. Phil. Soc, (3), 1981, 42-58. |
| [04] | Hoare, A. H. M.; An Embedding for groups with Length Function, Mathematika, 26, 1979, 99-102. |
| [05] | Hoare, A H M; On Length Functions and Nielson Methodsin FreeGroups, J. London Mathematical Society, (2), 14, 1976, 188-192. |
| [06] | Wlikens, D. L.; On Non Archimedian length in Groups, Mathematika, 23, 1976, (57-61). |
| [07] | Khanfar, M. M. I.; Combinatorial Properties of Groups with Length Function Ph. D. Thesis, University of Birmingham. U.K, 1978. |
| [08] | Meier, J.; Groups, Graphs and Trees, An Introduction to the Geometry of Infinite Groups, London Mathematical Society, 2008. |
| [09] | Lyndon, R. C. and Schupp, P. E. Combinatorial Group Theory, Springer-Verlag, Berlin, Heidelberg, New York, 1977. |
| [10] | Nesayef, F H, Groups generated by elements of length zero and one, Ph D Thesis, University of Birmingham, U K, 1983. |
