Triples of $2\times 2$ matrices which generate free groups
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- by S. Bachmuth and H. Mochizuki PDF
- Proc. Amer. Math. Soc. 59 (1976), 25-28 Request permission
Abstract:
A theorem is proved which guarantees that certain triples of $2 \times 2$ matrices over the complex numbers freely generate a free group. (There is no a priori reason that these matrices lie in a two generator matrix group.)References
- S. Bachmuth and H. Y. Mochizuki, Automorphisms of solvable groups, Bull. Amer. Math. Soc. 81 (1975), 420–422. MR 364452, DOI 10.1090/S0002-9904-1975-13767-0
- Orin Chein, Subgroups of $IA$ automorphisms of a free group, Acta Math. 123 (1969), 1–12. MR 255647, DOI 10.1007/BF02392382
- R. C. Lyndon and J. L. Ullman, Pairs of real $2$-by-$2$ matrices that generate free products, Michigan Math. J. 15 (1968), 161–166. MR 228593, DOI 10.1307/mmj/1028999969
- Wilhelm Magnus, Untersuchungen über einige unendliche diskontinuierliche Gruppen, Math. Ann. 105 (1931), no. 1, 52–74 (German). MR 1512704, DOI 10.1007/BF01455808
- I. N. Sanov, A property of a representation of a free group, Doklady Akad. Nauk SSSR (N. S.) 57 (1947), 657–659 (Russian). MR 0022557
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 59 (1976), 25-28
- MSC: Primary 20E05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0412272-4
- MathSciNet review: 0412272