Semigruppi, monodia e gruppi liberi
Parole chiave:
Semigruppi liberi, monoidi liberi, gruppi liberi, problema della parola, problema del coniugioAbstract
Lo scopo di questo articolo è quello di presentare l’esperienza svolta con docenti di matematica e studenti di 21 anni di età inerente alcune strutture algebriche astratte e osservare come questi concetti siano stati percepiti.
Riferimenti bibliografici
E. Artin, (1925). Theorie der Zöpfe, Abhandlungen aus dem Mathematischen, Abh. Math. Sem. Univ. Hamburg 4, 47-72, 2
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
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 — Aggiornato il 2020-07-15
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- 2020-07-15 (2)
- 2019-12-23 (1)
Come citare
Semigruppi, monodia e gruppi liberi. (2020). EDiMaST: Esperienze Didattiche Con Matematica, Scienze E Tecnologia, 5, 633–648. Recuperato da https://www.edimast.it/index.php/edimast/article/view/64 (Original work published 23 dicembre 2019)
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Articoli - Esperienze e Ricerca
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Copyright (c) 2019 Panagiote Ligouras
TQuesto lavoro è fornito con la licenza Creative Commons Attribuzione 4.0 Internazionale.
