On some free groups, generated by matrices

• Autorzy: Slanina P.
• Języki publikacji: EN

Słowa kluczowe

EN

combinatorial group; groups theory; matrices

PL

grupy; macierze

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 1
• Strony: 55--61
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Slanina P.

• Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland

Bibliografia

• [1] J. Bamberg, Non-free points for groups generated by a pair of 2x2 matrices, London Math. Soc. (2) 62, (2000), 795 -801.
• [2] A.F. Beardon, Pell's equation and two generator free Moebius groups, London Math. Soc. (1993), 527-532.
• [3] J.L. Brenner, Quelques groupes libres de matrices, C. R. Acad. Sci. Paris 241, (1955), 1689-1691.
• [4] B. Chang, S.A. Jennings, R. Ree, On certain matrices which generate free groups, Canadian J. Math. (1958), 279-284.
• [5] R.J. Evans, Non-free groups generated by two parabolic matrices, J. Res. Nat. Bur. Standards, vol. 84, no. 2, (1979), 179-180.
• [6] D.I. Fouxe-Rabinowitch, On a certain representation of a free group, Leningrad State Univ. Annals (Uchennye Zapiski). Math. Ser., 10 (1940), 154-157.
• [7] A. Grytczuk, M. Wojtowicz, The problem of freeness for Euler monoids and Moebius groups, Semigroup Forum 61 (2000), 277-282.
• [8] Yu.A. Ignatov, Free and nonfree subgroups of PSL2(C) that are generated by two parabolic elements, Mat. Sb. (N.S.) 106 (148), (1978), 372- 379.
• [9] Yu.A. Ignatov, Roots of unity as nonfree points of the complex plane, Mat. Zametki 27, (1980) no . 5, 825-827.
• [10] Yu.A. Ignatov , Rational nonfree points of the complex plane, Tulsk. Gos. Ped. Inst., Tula, ( 1986), 72-80.
• [11] Yu.A. Ignatov, Rational nonfree points of the complex plane, Tulsk. Gos. Ped . Inst., Tula, (1990), 53-59.
• [12] Yu.A. lgnatov, Rational nonfree points of the complex plane, part III, Tulsk. Gos. Ped. Inst., Tula, (1995), 78-84.
• [13] Yu.A. Ignatov, T.N. Gruzdeva, I.A. Sviridova, Free groups of linear-fractional transformations, Tulsk. Gos. Univ. Ser. Mat. Mekh. Inform. 5, (1999), 116-120.
• [14] M.I. Kabieniuk, Groups generated by two transitive matrices, Kemerovo State University, (1988).
• [15] R.C. Lyndon, P.E. Schupp, Combinatorial Group Theory, Springer-Verlag, Berlin-New York, (1977).
• [16] R.C. Lyndon, J.L. Ullman, Groups generated by two parabolic linear fractional transformations, Canadian J. Math. (1969), 1388-1403.
• [17] S.W. Lysenkov, Groups generated by two 2x2 matrices, Kemerovo State University, (1983) 27 -31.
• [18] W. Magnus, A. Karrass, D. Solitar, Combinatorial Group Theory, Dover Publications, Inc. New York, (1976).
• [19] M. Newman, A conjecture on a matrix group with tw genetators, J. Res. Nat. Bur. Standards, vol. 78B, no. 2, (1974), 69-70.
• [20] D.J.S. Robinson, A Course in the Theory of Groups, New York: Springer Verlag, (1996).
• [21] S. Saks, A. Zygmund, Analytic Functions, PWN Warszawa, (1965).
• [22] I.N. Sanov, Swojstwo odnowo priedstawlienia swobodnoj grupy, Dokl. Akad. Nauk SSSR 57 (7), Moskwa, (1947), 657-659.
• [23] A.I. Skuratskii, The problem of the generation of free groups by two unitriangular matrices, Mat. Zametki 24 (1978), 411-414.