On the finite subgroups of U(3) of order smaller than 512

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 39, 2010, Pages

  Ludl, Patrick Otto ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78649602803     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/39/395204     Document Type: Article

References (93)

1. Harrison P F, Perkins D H and Scott W G 2002 Tri-bimaximal mixing and the neutrino oscillation data Phys. Lett. B 530 167 (arXiv:hep-ph/0202074)
2. 13 > 0 arXiv:1001.4524
3. Maltoni M, Schwetz T, Tórtola M A and Valle J W F 2004 Status of global fits to neutrino oscillations New J. Phys. 6 122 (arXiv:hep-ph/0405172)
4. Fogli G L, Lisi E, Marrone A and Palazzo A 2006 Global analysis of three-flavor neutrino masses and mixings Prog. Part. Nucl. Phys. 57 742 (arXiv:hep-ph/0506083)
5. 13 > 0 from global neutrino data analysis Phys. Rev. Lett. 101 141801 (arXiv:0806.1649)
6. Schwetz T, Tortola M and Valle J W F 2008 Three-flavour neutrino oscillation update New J. Phys. 10 113011 (arXiv:0808.2016)
7. Albright C H 2009 Overview of neutrino mixing models and ways to differentiate among them arXiv:0905.0146
8. Ma E 2009 Neutrino mass: mechanisms and models arXiv:0905.0221
9. Altarelli G 2009 Theoretical models of neutrino mixing: recent developments Talk delivered at the 13th Int. Workshop on Neutrino Telescopes (Venice, 10-13 Mar. 2009) (arXiv:0905.2350)
10. Altarelli G and Feruglio F 2010 Discrete flavor symmetries and models of neutrino mixing arXiv:1002.0211
11. Miller G A, Blichfeldt L E and Dickson H F 1916 Theory and Applications of Finite Groups (New York: Wiley)
12. 3 and their application to the elementary-particle spectrum J. Math. Phys. 5 1038
13. 3 J. Math. Phys. 22 1543
14. Bovier A, Lüling M and Wyler D 1981 Representations and Clebsch-Gordan coefficients of Z-metacyclic groups J. Math. Phys. 22 1536
15. Fairbairn W M and Fulton T 1982 Some comments on finite subgroups of SU (3) J. Math. Phys. 23 1747
16. Frampton P H and Kephart T W 1995 Simple non-Abelian finite flavor groups and fermion masses Int. J. Mod. Phys. A 10 4689 (arXiv:hep-ph/9409330)
17. 2) J. Math. Phys. 48 073501 (arXiv:hep-th/0701188)
18. Luhn C, Nasri S and Ramond P 2007 Simple finite non-Abelian flavor groups J. Math. Phys. 48 123519 (arXiv:hep-th/0709.1447)
19. 2) J. Math. Phys. 50 013524 (arXiv:hep-th/0809.0639)
20. Blum A, Hagedorn C and Lindner M 2008 Fermion masses and mixings from dihedral flavor symmetries with preserved subgroups Phys. Rev. D 77 076004 (arXiv:hep-ph/0709.3450)
21. Ludl P O 2009 Systematic analysis of finite family symmetry groups and their application to the lepton sector arXiv:0907.5587
22. Zwicky R and Fischbacher T 2009 On discrete minimal flavour violation Phys. Rev. D 80 076009 (arXiv:0908.4182)
23. Ishimori H, Kobayashi T, Ohki H, Okada H, Shimizu Y and Tanimoto M 2010 Non-Abelian discrete symmetries in particle physics arXiv:1003.3552
24. The GAP Group 2008 GAP-Groups, Algorithms, and Programming, Version 4.4.12 http://www.gap-system.org
25. Besche H U, Eick B and O'Brien E A 2002 SmallGroups-a GAP package http://www.gap-system.org/Packages/sgl.html, http://www-public.tu-bs.de:8080/? beick/soft/small/small.html
26. Besche H U and Eick B 1999 Construction of finite groups J. Symb. Comput. 27 387
27. Besche H U and Eick B 1999 The groups of order at most 1000 except 512 and 768 J. Symb. Comput. 27 405
28. n × p Commun. Algebra 29 1759
29. Besche H U, Eick B and O'Brien E A 2001 The groups of order at most 2000 Electron. Res. Announc. Am. Math. Soc. 7 1
30. Besche H U, Eick B and O'Brien E A 2002 A millennium project: constructing small groups Int. J. Algebra Comput. 12 623
31. Eick B and O'Brien E A 1998 The groups of order 512 Proc. of the Abschlusstagung zum DFG Schwerpunkt Algorithmische Algebra und Zahlentheorie (Berlin: Springer) p 379
32. Eick B and O'Brien E A 1999 Enumerating p-groups J. Aust. Math. Soc. 67 191
33. 5 Staatsexamensarbeit, TU Braunschweig
34. 4 Math. Ann. 43 301
35. James R, Newman M F and O'Brien E A 1990 The groups of order 128 J. Algebra 129 136
36. Newman M F, O'Brien E A and Vaughan-Lee M R 2003 Groups and nilpotent Lie rings whose order is the sixth power of a prime J. Algebra 278 383
37. O'Brien E A 1990 The p-group generation algorithm J. Symb. Comput. 9 677
38. O'Brien E A 1991 The groups of order 256 J. Algebra 143 219
39. 7 for odd primep J. Algebra 292 243
40. Weisstein E W 2009 The CRC Encyclopedia of Mathematics (Boca Raton: Chapman & Hall/CRC)
41. 5) family symmetry and the golden ratio prediction for solar neutrino mixing arXiv:hep-ph/0812.1057
42. Grimus W and Ludl P O 2010 Principal series of finite subgroups of SU (3) arXiv: 1006.0098
43. Hamermesh M 1989 Group Theory and its Applications to Physical Problems (New York: Dover)
44. Ma E and Rajasekaran G 2001 Softly broken A4 symmetry for nearly degenerate neutrino masses Phys. Rev. D 64 113012 (arXiv:hep-ph/0106291)
45. 4 flavour symmetry breaking scheme for understanding quark and neutrino mixing angles arXiv:hep-ph/0601001
46. Altarelli G 2006 Models of neutrino masses and mixings arXiv:hep-ph/0611117
47. Ma E 2006 Application of finite groups to neutrino mass matrices arXiv:hep-ph/0612013
48. 4 model for lepton sector arXiv:0806.4592
49. Altarelli G and Meloni D 2009 A simplest A4 model for tri-bimaximal neutrino mixing arXiv:0905.0620
50. 3 Phys. Lett. B 652 27 (arXiv:0706.2341)
51. 7 and Σ (81) Phys. Rev. D 79 036002 (arXiv:0811.2955)
52. 4 as a natural flavor symmetry for lepton mixing arXiv:hep-ph/0811.0345
53. 4 flavor symmetry and fermion masses: towards a grand unified theory of flavor J. High Energy Phys. JHEP 06 (2006) 042 (arXiv:hep-ph/0602244)
54. Branco G C, Gerard J-M and Grimus W 1984 Geometrical T-violation Phys. Lett. B 136 383
55. de Medeiros Varzielas I, King S F and Ross G G 2007 Neutrio tri-bi-maximal mixing from a non-Abelian discrete family symmetry Phys. Lett. B 648 201 (arXiv:hep-ph/0607045)
56. Ma E 2008 Near tribimaximal neutrio mixing with Δ (27) symmetry Phys. Lett. B 660 505 (arXiv:0709.0507)
57. Ma E 2006 Neutrino mass matrix from Δ (27) symmetry Mod. Phys. Lett. A 21 1917 (arXiv:hep-ph/0607056)
58. Kobayashi T, Nilles H P, Plöger F, Raby S and Ratz M 2007 Stringy origin of non-Abelian discrete flavor symmetries Nucl. Phys. B 768 135 (arXiv:hep-ph/0611020)
59. Grimus W and Lavoura L 2009 Tri-bimaximal mixing from symmetry only J. High Energy Phys. JHEP 04 (2009) 013 (arXiv:0811.4766)
60. Ishimori H, Kobayashi T, Okada H, Shimizu Y and Tanimoto M 2009 Lepton flavor model from Δ (54) symmetry J. High Energy Phys. JHEP 04 (2009) 011 (arXiv:0811.4683)
61. King S F and Luhn C 2009 A new family symmetry for SO (10) GUTs arXiv:0905.1686
62. Ma E 2007 Lepton family symmetry and possible application to the Koide mass formula Phys. Lett. B 649 287 (arXiv:hep-ph/0612022)
63. Ma E 2007 New lepton family symmetry and neutrino tribimaximal mixing Europhys. Lett. 79 61001 (arXi v:hep-ph/0701016)
64. Yamanaka Y, Sugawara H and Pakvasa S 1982 Permutation symmetries and the fermion mass matrix Phys. Rev. D 25 1895
65. Yamanaka Y, Sugawara H and Pakvasa S 1984 Permutation symmetries and the fermion mass matrix Phys. Rev. D 29 2135 (erratum)
66. 4 model of permutation symmetry Phys. Rev. D 30 255
67. Ozaki H 1989 Four-generation model based on an S4 permutation symmetry Phys. Rev. D 40 2425
68. 4 scenario for naturally degenerate neutrinos Phys. Lett. B 329 463 (arXiv:hep-ph/9403201)
69. 4 symmetry Phys. Lett. B 632 352 (arXiv:hep-ph/0508231)
70. 4 Int. J. Mod. Phys. A 22 2469 (arXiv:hep-ph/0611078)
71. 4 flavor symmetry Phys. Rev. D 74 115005 (arXiv:hep-ph/0608022)
72. 2 symmetry and neutrino mixing Phys. Lett. B 655 132 (arXiv:hep-ph/0612214)
73. 4 flavor symmetry embedded into SU (3) and lepton masses and mixing J. High Energy Phys. JHEP 08 (2007) 086 (arXiv:0705.2275)
74. Lam C S 2007 Symmetry of lepton mixing Phys. Lett. B 656 193 (arXiv:0708.3665)
75. Lam C S 2008 Determining horizontal symmetry from neutrino mixing Phys. Rev. Lett. 101 121602 (arXiv:0804.2622)
76. 4 Phys. Rev. D 78 053004 (arXiv:0804.4571)
77. Lam C S 2008 The unique horizontal symmetry of leptons Phys. Rev. D 78 073015 (arXiv:0809.1185)
78. 4 flavor symmetry of quarks and leptons in SU (5) GUT Prog. Theor. Phys. 121 769 (arXiv:0812.5031)
79. 4 based model Nucl. Phys. B 816 204 (arXiv:0901.2086)
80. 4 based models arXiv:0902.2849
81. 4 discrete symmetry J. High Energy Phys. JHEP 05 (2009) 020 (arXiv:0903.1940)
82. 4 flavor model of quarks and leptons Talk given at the 16th Yukawa International Seminar: Particle Physics beyond the Standard Model (Kyoto, 26 Jan-25 Mar. 2009) arXiv:0904.2450
83. 4 the horizontal symmetry of tri-bimaximal lepton mixing? J. Phys. G: Nucl. Part. Phys. 36 115007 (arXiv:0906.2689)
84. Ding G J 2010 Fermion masses and flavor mixings in a model with S4 flavor symmetry Nucl. Phys. B 827 82 (arXiv:0909.2210)
85. 4 discrete symmetry AIP Conf. Proc. 1200 948 (arXiv:0909.2760)
86. 2 flavor symmetry in supersymmetric extra U (1) model arXiv:0910.3370
87. 4 model for fermion masses and mixings J. Phys. G: Nucl. Part. Phys. 37 055201 (arXiv:0911.3591)
88. 4 flavor symmetries arXiv:0911.4799
89. de Adelhart Toorop R 2010 Family physics with S (4) and Pati-Salam Prog. Part. Nucl. Phys. 64 318
90. 4 model for quarks and leptons with maximal atmospheric angle Phys. Rev. D 81 085015 (arXiv:1001.2265)
91. 4 × SU (5) to NLO arXiv:1003.4249
92. 4 symmetry arXiv:1004.3469 [hep-ph]
93. 4 flavor model with SUSY arXiv:1004.5004