AASCIT - Journal - All Issues

American Journal of Mathematical and Computational Sciences

The Journal

Indexing

Manuscript Information

Classifications of Some Groups with Length Functions

American Journal of Mathematical and Computational Sciences
Vol.1 , No. 3, Publication Date: Aug. 21, 2017, Page: 89-93

201 Views Since August 21, 2017, 161 Downloads Since Aug. 21, 2017

Paper in PDF (232K)

Follow on

Authors

[1]	Faisal Hussain Nesayef, Department of Mathematics, Faculty of Science, University of Kirkuk, Kirkuk, Iraq.

Abstract

The concept of length functions on groups was first introduced by Lyndon [1]. Subsequently many other researchers worked in this field which resulted in adding further axioms in connection to the original axioms set by Lyndon. These new axioms additional axioms and conditions enabled the other researchers to achieve remarkable new results or to give direct proofs of many other cases. This procedure has given motivation to the researchers to enter new domains within the field of Combinatorial Group Theory.

Keywords

Archimedean Elements, Free Group, Free Product of Groups, Free Product with Amalgamation, HNN Extension, Quasi-HNN Extension, Length Function, Unique Extension

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.; Embedding Theorems, Math. Proc. Cambridge Phil. Soc., 1979, 85, 417-429.
[04]	Chiswell, I. M.; Length Function and Free products with amalgamation of groups´, Math. Proc. Camb. Phil. Soc, (3), 1981, 42-58.
[05]	Hoare, A. H. M.; An Embedding for groups with Length Function, Mathematika, 26, 1979, 99-102.
[06]	Hoare, A. H. M.; On Length Functions and Nielson Methods in Free Groups, J. London Mathematical Society, (2), 14, 1976, 188-192.
[07]	Wlikens, D. L.; On Non Archimedian length in Groups, Mathematika, 23, 1976, (57-61).
[08]	Lyndon, R. C., Schupp, P. E.: Combinatorial Group Theory, Springler Verlag, Berlin, Heidelberg, 2001
[09]	Khanfar, M. M. I.; Combinatorial Properties of Groups with Length Function Ph.D. Thesis, University of Birmingham. U.K, 1978.
[10]	Nesayef, F. H.; Length Functions on Free product with amalgamation, International Journal of Recent Scientific research, Vol. 4, Issue 11, 2013, (1697-1700).
[11]	Nesayef, F. H.; Presentation of groups generated by elements of length zero and one, International journal of Mathematics and Computer Applications Research, Vol.4, Issue 6, 2014, (45-52).