Freeness of the group ‹an, bn› for some integer n, a, b∈SL(2, C)

Abdul MAJEED

doi:10.2969/jmsj/02910029

Freeness of the group ‹aⁿ, bⁿ› for some integer n, a, b∈SL(2, C)

Abdul MAJEED

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ジャーナルフリー

1977 年 29 巻 1 号 p. 29-33

DOI https://doi.org/10.2969/jmsj/02910029

詳細

Published: 1977 Received: 1975/05/28 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文タイトル訂正内容: Wrong : Freeness of the group <aⁿ, bⁿ> for some integer n, a, b∈SL(2, C)
Right : Freeness of the group ‹aⁿ, bⁿ› for some integer n, a, b∈SL(2, C)

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) B. Chang, S. A. Jennings and R. Ree, On certain pairs of matrices which generate free groups, Canad. J. Math., 10 (1958), 279-284. M. R. 20 #906.
2) J. D. Dixon, The structure of linear groups, Von Nostrand, New York, 1973.
3) R. C. Lyndon and J. L. Ullman, Pairs of 2-by-2 matrices that generate free products, Michigan J. Math., 21 (1969), 161-166. M. R. 37 #4173.
4) A. M. Macbeath, Packings, free products and residually finite groups, Proc. Cambridge Philos. Soc., 59 (1963), 555-558.
5) A. Majeed, Reducible and irreducible 2-generator subgroups of SL(2, C), to appear in P. U. J. Math. (Lahore) Pakistan.
6) A. Majeed, Two generator subgroups of SL(2, C), Ph. D. Thesis submitted to Carleton University, Ottawa, 1974.
7) N. Purzitsky, Two generator discrete free products of groups, Math. Z., 126 (1972), 209-223.
8) N. Purzitsky, Real two dimensional representations of two generator free groups, Math. Z., 127 (1972), 95-104.
9) G. Rosenberger, Fuchsche Gruppen, die freies Produkt Zweier Zyklischer Gruppen sind, und die Gleichung x²+y²+z²=xyz, Math. Ann., 199 (1972), 213-227.
10) B. A. F. Wehrfritz, Infinite linear groups, Springer-Verlag, New York, 1973.

Right : [1] B. Chang, S. A. Jennings and R. Ree, On certain pairs of matrices which generate free groups, Canad. J. Math., 10 (1958), 279-284. M. R. 20 #906.
[2] J. D. Dixon, The structure of linear groups, Von Nostrand, New York, 1973.
[3] R. C. Lyndon and J. L. Ullman, Pairs of 2-by-2 matrices that generate free products, Michigan J. Math., 21 (1969), 161-166. M. R. 37 #4173.
[4] A. M. Macbeath, Packings, free products and residually finite groups, Proc. Cambridge Philos. Soc., 59 (1963), 555-558.
[5] A. Majeed, Reducible and irreducible 2-generator subgroups of SL(2, C), to appear in P. U. J. Math. (Lahore) Pakistan.
[6] A. Majeed, Two generator subgroups of SL(2, C), Ph. D. Thesis submitted to Carleton University, Ottawa, 1974.
[7] N. Purzitsky, Two generator discrete free products of groups, Math. Z., 126 (1972), 209-223.
[8] N. Purzitsky, Real two dimensional representations of two generator free groups, Math. Z., 127 (1972), 95-104.
[9] G. Rosenberger, Fuchsche Gruppen, die freies Produkt Zweier Zyklischer Gruppen sind, und die Gleichung x²+y²+z²=xyz, Math. Ann., 199 (1972), 213-227.
[10] B. A. F. Wehrfritz, Infinite linear groups, Springer-Verlag, New York, 1973.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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