Some Applications of Free Group

Yıl 2020, Cilt: 3 Sayı: 1, 27 - 34, 17.09.2020

Majid Abed , Hekmat Mustafa

Öz

In this paper, we study many concepts as applications of free group, for example, presentation, rank of free group, and inverse of free group. We discussed some results about presentation concept and related it with free group. The our main result about free rank, is if G is a group, then G is free rank n if and only if G≅Zn. Also we obtained a new fact about inverse semigroup which say there is no free inverse semigroup is finitely generated as a semigroup. Moreover, we studied some results of inverse of free semigroup, These were illustrated by formulating Theorems, Lemma, Corollaries, and all of these concepts were explained through detailed examples.

Anahtar Kelimeler

Free group, Rank free group, Inverse free semigroup

Kaynakça

• [1] B.Sury, Free groups – basics, Stat-Math Unit Indian Statistical Institute Bangalore, India, IIT Bombay, 2010.
• [2] B. Baumslag and B. Chandler, Outline of Theory and Problems of Group Theory, New York University, Schaum's Outline Series, Mcgraw-Hill Book Company, New York, San Francisco, Toronto, Sydney, 1986.
• [3] J. Z. Gon¸calves and D. S. Passman, Linear groups and group rings, J. Algebra 295 2006, 94–118.
• [4] C. F. Miller,Combinatorial Group Theory III, Australian National University, 2004.
• [5] A. I. Maltsev, On the equation zxyx−1 y−1 z−1 = aba−1 b−1 in a free group, Algebra and Logic, 1(5) 1962, 45-50.
• [6] J. L. Dyer and G. P. Scott, Periodic automorphisms of free groups, Comm. Alg., 3 1975, 195-201.
• [7] S. Meskin, Periodic automorphisms of the two-generator free group, in: Proc. Conf. Canberra, 1973 (Lecture Notes in Math., 372 (1974), 494-498). Berlin: Springer.