Semigroups, monoids and free groups
Keywords:
Free Semigroups, free monoids, free groups, word problem, conjugacy problemAbstract
The purpose of this paper is to present the experience with mathematics teachers and students of 21 years of age concerning some abstract algebraic structures and to observe how these concepts have been perceived.
References
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O. Bogopolski, (2008). Introduction to Group Theory, European Mathematical Society Publishing House, Zürich, 31 W.W. Boone, (1959). The word problem. Ann. of Math. (2) 70, 207–265, 35
M. Dehn. (1911). Über unendliche diskontinuierliche Gruppen, Math. Ann., 71(1), 116–144, 54
S. Dey, K. Gongopadhyay, 2018. Commutator subgroups of welded braid groups, Topology Appl., 237: 7–20, 128 F.A. Garside, (1969). The braid group and other groups, Quart. J. Math. Oxford Ser. 20, 235–254, 45
L. Greenberg, (1960). Discrete groups of motions, Canad. J. Math. 12, 414-425, 63
D.L. Johnson, (1997). Presentations of groups, Cambridge University Press, United Kingdom, 85
E.-K. Lee, (2010). A positive presentation for the pure braid group, Journal of the Chungcheong Mathematical Society, Vol. 23, No. 3, pp. 555-561, 47
F.W. Levi, (1930). Über die Untergruppen der freien Gruppen I, Math. Z. 32, 315-318, 61
F.W. Levi, (1933). Über die Untergruppen der freien Gruppen II, Math. Z. 37, 90-97, 62
R.C. Lyndon, P.E. Schupp, (1977). Combinatorial group theory, Springer-Verlag, Berlin, Heidelberg, New York, 60
W. Magnus, A. Karrass, D. Solitar, (1976). Combinatorial group theory, Dover Publ. Inc., NewYork, 33
S. Moran, (1983). The Mathematical Theory of Knots and Braids, North–Holland Mathematics Studies, vol. 82, Elsevier, Amsterdam, 82
B.H. Neumann, (1937). Some remarks on infinite groups. J. London Math. Soc. 12, 120–127, 34
P.S. Novikov, (1958). On the algorithmic insolvability of the word problem in group theory, Trudy Mat. Inst. Steklov. 44 (1955), 3–143; English transl. Amer. Math. Soc. Transl. (2) 9, Amer. Math. Soc., Providence, RI, 1–122, 36
D.J.S. Robinson, (2003). An introduction to abstract algebra, Walter de Gruyter, Berlin, 59 J.J. Rotman, (1995). An introduction to the theory of groups, 4 th ed., Springer-Verlag New York, Ine, 86
V. Vershinin, (2010). On the singular braid monoid, St. Petersburg Math. J., Vol. 21, No. 5, pp. 693-704, 44
G. Baumslag, (1976). Multiplicators and metabelian groups, J. Austral. Math. Soc. Ser. A 22, 305–312, 32
O. Bogopolski, (2008). Introduction to Group Theory, European Mathematical Society Publishing House, Zürich, 31 W.W. Boone, (1959). The word problem. Ann. of Math. (2) 70, 207–265, 35
M. Dehn. (1911). Über unendliche diskontinuierliche Gruppen, Math. Ann., 71(1), 116–144, 54
S. Dey, K. Gongopadhyay, 2018. Commutator subgroups of welded braid groups, Topology Appl., 237: 7–20, 128 F.A. Garside, (1969). The braid group and other groups, Quart. J. Math. Oxford Ser. 20, 235–254, 45
L. Greenberg, (1960). Discrete groups of motions, Canad. J. Math. 12, 414-425, 63
D.L. Johnson, (1997). Presentations of groups, Cambridge University Press, United Kingdom, 85
E.-K. Lee, (2010). A positive presentation for the pure braid group, Journal of the Chungcheong Mathematical Society, Vol. 23, No. 3, pp. 555-561, 47
F.W. Levi, (1930). Über die Untergruppen der freien Gruppen I, Math. Z. 32, 315-318, 61
F.W. Levi, (1933). Über die Untergruppen der freien Gruppen II, Math. Z. 37, 90-97, 62
R.C. Lyndon, P.E. Schupp, (1977). Combinatorial group theory, Springer-Verlag, Berlin, Heidelberg, New York, 60
W. Magnus, A. Karrass, D. Solitar, (1976). Combinatorial group theory, Dover Publ. Inc., NewYork, 33
S. Moran, (1983). The Mathematical Theory of Knots and Braids, North–Holland Mathematics Studies, vol. 82, Elsevier, Amsterdam, 82
B.H. Neumann, (1937). Some remarks on infinite groups. J. London Math. Soc. 12, 120–127, 34
P.S. Novikov, (1958). On the algorithmic insolvability of the word problem in group theory, Trudy Mat. Inst. Steklov. 44 (1955), 3–143; English transl. Amer. Math. Soc. Transl. (2) 9, Amer. Math. Soc., Providence, RI, 1–122, 36
D.J.S. Robinson, (2003). An introduction to abstract algebra, Walter de Gruyter, Berlin, 59 J.J. Rotman, (1995). An introduction to the theory of groups, 4 th ed., Springer-Verlag New York, Ine, 86
V. Vershinin, (2010). On the singular braid monoid, St. Petersburg Math. J., Vol. 21, No. 5, pp. 693-704, 44
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2019-12-23 — Updated on 2020-07-15
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Semigroups, monoids and free groups. (2020). EDiMaST: Experiences of Teaching With Mathematics, Sciences and Technology, 5, 633–648. Retrieved from https://www.edimast.it/index.php/edimast/article/view/64 (Original work published December 23, 2019)
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Copyright (c) 2019 Panagiote Ligouras
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