Let be real Möbius groups. For any 2×2 matrix A in induces real Möbius transformations g by the formula where . The collection of all real Möbius transformations for which takes the values 1 forms a group which can be identified with . We write to mean that f is a random variable in. In this paper, we study the random Möbius subgroup. We can get some new results: (1) If, the probability is greater than 0.027282. (2) If f is hyperbolic transformation and g is parabolic transformation, then the probability is discrete is greater than 7/12. (3) If f is elliptic of order n and g is elliptic of order 2, then the probability is discrete is greater than 2/n. (4) The probability that random chosen generate an elementary or non-discrete groupis greater than 0.0302049.
Published in | Applied and Computational Mathematics (Volume 11, Issue 1) |
DOI | 10.11648/j.acm.20221101.13 |
Page(s) | 31-37 |
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Random Discrete Möbius Group, , Jørgensen’s Inequality
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APA Style
Binlin Dai, Zekun Li. (2022). Discrete Probability of Random Möbius Groups: Random Subgroups by Two Generators. Applied and Computational Mathematics, 11(1), 31-37. https://doi.org/10.11648/j.acm.20221101.13
ACS Style
Binlin Dai; Zekun Li. Discrete Probability of Random Möbius Groups: Random Subgroups by Two Generators. Appl. Comput. Math. 2022, 11(1), 31-37. doi: 10.11648/j.acm.20221101.13
AMA Style
Binlin Dai, Zekun Li. Discrete Probability of Random Möbius Groups: Random Subgroups by Two Generators. Appl Comput Math. 2022;11(1):31-37. doi: 10.11648/j.acm.20221101.13
@article{10.11648/j.acm.20221101.13, author = {Binlin Dai and Zekun Li}, title = {Discrete Probability of Random Möbius Groups: Random Subgroups by Two Generators}, journal = {Applied and Computational Mathematics}, volume = {11}, number = {1}, pages = {31-37}, doi = {10.11648/j.acm.20221101.13}, url = {https://doi.org/10.11648/j.acm.20221101.13}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20221101.13}, abstract = {Let be real Möbius groups. For any 2×2 matrix A in induces real Möbius transformations g by the formula where . The collection of all real Möbius transformations for which takes the values 1 forms a group which can be identified with . We write to mean that f is a random variable in. In this paper, we study the random Möbius subgroup. We can get some new results: (1) If, the probability is greater than 0.027282. (2) If f is hyperbolic transformation and g is parabolic transformation, then the probability is discrete is greater than 7/12. (3) If f is elliptic of order n and g is elliptic of order 2, then the probability is discrete is greater than 2/n. (4) The probability that random chosen generate an elementary or non-discrete groupis greater than 0.0302049.}, year = {2022} }
TY - JOUR T1 - Discrete Probability of Random Möbius Groups: Random Subgroups by Two Generators AU - Binlin Dai AU - Zekun Li Y1 - 2022/02/19 PY - 2022 N1 - https://doi.org/10.11648/j.acm.20221101.13 DO - 10.11648/j.acm.20221101.13 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 31 EP - 37 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20221101.13 AB - Let be real Möbius groups. For any 2×2 matrix A in induces real Möbius transformations g by the formula where . The collection of all real Möbius transformations for which takes the values 1 forms a group which can be identified with . We write to mean that f is a random variable in. In this paper, we study the random Möbius subgroup. We can get some new results: (1) If, the probability is greater than 0.027282. (2) If f is hyperbolic transformation and g is parabolic transformation, then the probability is discrete is greater than 7/12. (3) If f is elliptic of order n and g is elliptic of order 2, then the probability is discrete is greater than 2/n. (4) The probability that random chosen generate an elementary or non-discrete groupis greater than 0.0302049. VL - 11 IS - 1 ER -