[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.
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.
[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.
Abed, M., & Mustafa, H. (2020). Some Applications of Free Group. Journal of Multidisciplinary Modeling and Optimization, 3(1), 27-34.
AMA
Abed M, Mustafa H. Some Applications of Free Group. jmmo. Eylül 2020;3(1):27-34.
Chicago
Abed, Majid, ve Hekmat Mustafa. “Some Applications of Free Group”. Journal of Multidisciplinary Modeling and Optimization 3, sy. 1 (Eylül 2020): 27-34.
EndNote
Abed M, Mustafa H (01 Eylül 2020) Some Applications of Free Group. Journal of Multidisciplinary Modeling and Optimization 3 1 27–34.
IEEE
M. Abed ve H. Mustafa, “Some Applications of Free Group”, jmmo, c. 3, sy. 1, ss. 27–34, 2020.
ISNAD
Abed, Majid - Mustafa, Hekmat. “Some Applications of Free Group”. Journal of Multidisciplinary Modeling and Optimization 3/1 (Eylül 2020), 27-34.
JAMA
Abed M, Mustafa H. Some Applications of Free Group. jmmo. 2020;3:27–34.
MLA
Abed, Majid ve Hekmat Mustafa. “Some Applications of Free Group”. Journal of Multidisciplinary Modeling and Optimization, c. 3, sy. 1, 2020, ss. 27-34.
Vancouver
Abed M, Mustafa H. Some Applications of Free Group. jmmo. 2020;3(1):27-34.