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Journal articles on the topic 'Groupes de triangle'

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Published: 4 June 2021

Last updated: 13 February 2022

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1

Allcock, Daniel. "Triangles of Baumslag–Solitar Groups." Canadian Journal of Mathematics 64, no. 2 (2012): 241–53. http://dx.doi.org/10.4153/cjm-2011-062-8.

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Abstract Our main result is that many triangles of Baumslag–Solitar groups collapse to finite groups, generalizing a famous example of Hirsch and other examples due to several authors. A triangle of Baumslag–Solitar groups means a group with three generators, cyclically ordered, with each generator conjugating some power of the previous one to another power. There are six parameters, occurring in pairs, and we show that the triangle fails to be developable whenever one of the parameters divides its partner, except for a few special cases. Furthermore, under fairly general conditions, the group

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2

Baumslag, Gilbert, John W. Morgan, and Peter B. Shalen. "Generalized triangle groups." Mathematical Proceedings of the Cambridge Philosophical Society 102, no. 01 (1987): 25. http://dx.doi.org/10.1017/s0305004100067013.

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3

Sridevi, P. "A Note on Detection of Communities in Social Networks." International Journal of Engineering and Computer Science 9, no. 03 (2020): 24978–83. http://dx.doi.org/10.18535/ijecs/v9i03.4452.

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The modern Science of Social Networks has brought significant advances to our understanding of the Structure, dynamics and evolution of the Network. One of the important features of graphs representing the Social Networks is community structure. The communities can be considered as fairly independent components of the social graph that helps identify groups of users with similar interests, locations, friends, or occupations. The community structure is closely tied to triangles and their count forms the basis of community detection algorithms. The present work takes into consideration, a triang

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4

PINSKY, TALI. "Templates for geodesic flows." Ergodic Theory and Dynamical Systems 34, no. 1 (2012): 211–35. http://dx.doi.org/10.1017/etds.2012.132.

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AbstractWe construct templates for geodesic flows on an infinite family of Hecke triangle groups. Our results generalize those of E. Ghys [Knots and dynamics. Proc. Int. Congress of Mathematicians. Vol. 1. International Congress of Mathematicians, Zürich, 2007], who constructed a template for the modular flow in the complement of the trefoil knot in $S^3$. A significant difficulty that arises in any attempt to go beyond the modular flow is the fact that for other Hecke triangles the geodesic flow cannot be viewed as a flow in $S^3$, and one is led to consider embeddings into lens spaces. Our f

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5

Howie, J., V. Metaftsis, and R. M. Thomas. "Finite generalized triangle groups." Transactions of the American Mathematical Society 347, no. 9 (1995): 3613–23. http://dx.doi.org/10.1090/s0002-9947-1995-1303121-7.

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6

PRUNESCU, MIHAI. "RECURRENT TWO-DIMENSIONAL SEQUENCES GENERATED BY HOMOMORPHISMS OF FINITE ABELIAN p-GROUPS WITH PERIODIC INITIAL CONDITIONS." Fractals 19, no. 04 (2011): 431–42. http://dx.doi.org/10.1142/s0218348x1100552x.

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We prove that if a recurrent two-dimensional sequence with periodic initial conditions coincides in a sufficiently large starting square with a two-dimensional sequence produced by an expansive system of context-free substitutions, then they must coincide everywhere. We apply this result for some examples built up by homomorphisms of finite abelian p-groups, in particular for Pascal's Triangle modulo pk, Pascal's Triangles modulo 2 with non-trivial periodic borders, and Sierpinski's Carpets with non-trivial periodic border. All these particular cases justify the conjecture that recurrent two-d

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7

Chermak, Andrew. "Triangles of groups." Transactions of the American Mathematical Society 347, no. 11 (1995): 4533–58. http://dx.doi.org/10.1090/s0002-9947-1995-1316847-6.

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8

Vsemirnov, Maxim, Vitaliy Mysovskikh, and M. Chiara Tamburini. "Triangle Groups as Subgroups of Unitary Groups." Journal of Algebra 245, no. 2 (2001): 562–83. http://dx.doi.org/10.1006/jabr.2001.8945.

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9

LEVITT, RENA, and JON MCCAMMOND. "TRIANGLES, SQUARES AND GEODESICS." International Journal of Algebra and Computation 22, no. 05 (2012): 1250041. http://dx.doi.org/10.1142/s0218196712500415.

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In the early 1990s Steve Gersten and Hamish Short proved that compact nonpositively curved triangle complexes have biautomatic fundamental groups and that compact nonpositively curved square complexes have biautomatic fundamental groups. In this paper we report on the extent to which results such as these extend to nonpositively curved complexes built out a mixture of triangles and squares. Since both results by Gersten and Short have been generalized to higher dimensions, this can be viewed as a first step towards unifying Januszkiewicz and Świȧtkowski's theory of simplicial nonpositive curva

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10

Levai, L., G. Rosenberger, and B. Souvignier. "All Finite Generalized Triangle Groups." Transactions of the American Mathematical Society 347, no. 9 (1995): 3625. http://dx.doi.org/10.2307/2155029.

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11

Hagelberg, M., C. MacLachlan, and G. Rosenberger. "On discrete generalised triangle groups." Proceedings of the Edinburgh Mathematical Society 38, no. 3 (1995): 397–412. http://dx.doi.org/10.1017/s0013091500019210.

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A generalised triangle group has a presentation of the formwhere R is a cyclically reduced word involving both x and y. When R = xy, these classical triangle groups have representations as discrete groups of isometrics of S2, R2, H2 depending onIn this paper, for other words R, faithful discrete representations of these groups in Isom +H3 = PSL(2, C) are considered with particular emphasis on the case R = [x, y] and also on the relationship between the Euler characteristic χ and finite covolume representations.

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12

Lévai, L., G. Rosenberger, and B. Souvignier. "All finite generalized triangle groups." Transactions of the American Mathematical Society 347, no. 9 (1995): 3625–27. http://dx.doi.org/10.1090/s0002-9947-1995-1303124-2.

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13

Wilson, J. "Simple images of triangle groups." Quarterly Journal of Mathematics 50, no. 200 (1999): 523–31. http://dx.doi.org/10.1093/qjmath/50.200.523.

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14

Doran, Charles F., Terry Gannon, Hossein Movasati, and Khosro M. Shokri. "Automorphic forms for triangle groups." Communications in Number Theory and Physics 7, no. 4 (2013): 689–737. http://dx.doi.org/10.4310/cntp.2013.v7.n4.a4.

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15

Martin, Gaven J. "Triangle subgroups of Kleinian groups." Commentarii Mathematici Helvetici 71, no. 1 (1996): 339–61. http://dx.doi.org/10.1007/bf02566424.

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16

Fried, David. "Symbolic dynamics for triangle groups." Inventiones Mathematicae 125, no. 3 (1996): 487–521. http://dx.doi.org/10.1007/s002220050084.

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17

Zhu, Qiuliang, Bengong Shi, Bin Xu, and Jianfeng Yuan. "Obtuse triangle screw configuration for optimal internal fixation of femoral neck fracture: an anatomical analysis." HIP International 29, no. 1 (2018): 72–76. http://dx.doi.org/10.1177/1120700018761300.

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Objectives: To identify the optimal screw configuration for internal fixation of femoral neck fractures based on anatomic analysis on radiologic imaging. Methods: 30 proximal femurs of 15 adults were constructed by CT. 3 femoral neck sections (FNS), the subcapital, medial, and the fundus, were projected on to the lateral femoral trochanteric wall. The simulated 3 screw configurations in the projection of FNS include: 2 inverted equilateral triangles symmetrised to the axis of the FNS (IET-FNS group) or the coronal axis of the proximal femur (IET-PR group) and an obtuse triangle (OT group). The

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18

Alperin, Roger C. "Platonic Triangles of Groups." Experimental Mathematics 7, no. 3 (1998): 191–219. http://dx.doi.org/10.1080/10586458.1998.10504369.

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19

Maclachlan, Colin. "Triangle subgroups of hyperbolic tetrahedral groups." Pacific Journal of Mathematics 176, no. 1 (1996): 195–203. http://dx.doi.org/10.2140/pjm.1996.176.195.

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20

Rosenberger, G. "Free subgroups of generalized triangle groups." Algebra and Logic 28, no. 2 (1989): 152–61. http://dx.doi.org/10.1007/bf01979378.

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21

Williams, Alun G. T. "Arithmeticity of orbifold generalised triangle groups." Journal of Pure and Applied Algebra 177, no. 3 (2003): 309–22. http://dx.doi.org/10.1016/s0022-4049(02)00180-9.

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22

Kamiya, Shigeyasu, John R. Parker, and James M. Thompson. "Notes on complex hyperbolic triangle groups." Conformal Geometry and Dynamics of the American Mathematical Society 14, no. 12 (2010): 202. http://dx.doi.org/10.1090/s1088-4173-2010-00215-8.

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23

Karaduman, Erdal, and Ömür Deveci. "K-nacciSequences in Finite Triangle Groups." Discrete Dynamics in Nature and Society 2009 (2009): 1–10. http://dx.doi.org/10.1155/2009/453750.

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Ak-nacci sequencein a finite group is a sequence of group elementsx0,x1,x2,…,xn,…for which, given an initial (seed) setx0,x1,x2,…,xj−1, each element is defined byxn=x0x1…xn−1, for j≤n<k, and xn=xn−kxn−k+1…xn−1, for n≥k.We also require that the initial elements of the sequence,x0,x1,x2,…,xj−1, generate the group, thus forcing thek-naccisequence to reflect the structure of the group. TheK-naccisequence of a group generated byx0,x1,x2,…,xj−1is denoted byFk(G;x0,x1,…,xj−1)and its period is denoted byPk(G;x0,x1,…,xj−1). In this paper, we obtain the period ofK-naccisequences in finite polyhedral

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24

Vulakh, L. Ya. "The Markov Spectra for Triangle Groups." Journal of Number Theory 67, no. 1 (1997): 11–28. http://dx.doi.org/10.1006/jnth.1997.2181.

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25

Pratoussevitch, Anna. "Traces in Complex Hyperbolic Triangle Groups." Geometriae Dedicata 111, no. 1 (2005): 159–85. http://dx.doi.org/10.1007/s10711-004-1493-0.

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26

Grossi, Carlos H. "On the type of triangle groups." Geometriae Dedicata 130, no. 1 (2007): 137–48. http://dx.doi.org/10.1007/s10711-007-9209-x.

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27

Xu, Mengmeng, Jieyan Wang, and Baohua Xie. "Complex hyperbolic (3,n,∞) triangle groups." Journal of Mathematical Analysis and Applications 492, no. 1 (2020): 124409. http://dx.doi.org/10.1016/j.jmaa.2020.124409.

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28

Stover, Matthew. "Arithmeticity of complex hyperbolic triangle groups." Pacific Journal of Mathematics 257, no. 1 (2012): 243–56. http://dx.doi.org/10.2140/pjm.2012.257.243.

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29

Parker, John R., Jieyan Wang, and Baohua Xie. "Complex hyperbolic (3,3,n) triangle groups." Pacific Journal of Mathematics 280, no. 2 (2016): 433–53. http://dx.doi.org/10.2140/pjm.2016.280.433.

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30

Goodman, Samantha, Lana Vanderlee, Rachel Acton, Syed Mahamad, and David Hammond. "The Impact of Front-of-Package Label Design on Consumer Understanding of Nutrient Amounts." Nutrients 10, no. 11 (2018): 1624. http://dx.doi.org/10.3390/nu10111624.

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A between-groups experiment examined the salience of front-of-package (FOP) symbols. Adults from Canada, the US, Australia, and the UK completed an online survey (n = 11,617). Respondents were randomized to view cereal boxes displaying one of 11 FOP label conditions for ‘high’ levels of sugar and saturated fat: control (no FOP symbol), red circle, red ‘stop sign’, magnifying glass, magnifying glass + exclamation mark, and ‘caution’ triangle + exclamation mark, plus each of these five conditions accompanied by a ‘high in’ text descriptor. Participants identified the amount of saturated fat and

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31

Zhao, Xiaochun, Mohamed Labib, Dinesh Ramanathan, et al. "The anterior incisural width as a preoperative indicator for intradural space evaluation: An anatomical investigation." Surgical Neurology International 11 (July 25, 2020): 207. http://dx.doi.org/10.25259/sni_175_2020.

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Background: The opticocarotid triangle (OCT) and the carotico-oculomotor triangle (COT) are two anatomical triangles used in accessing the interpeduncular region. Our objective is to evaluate if the anterior incisural width (AIW) is an indicator to predict the intraoperative exposure through both triangles. Methods: Twenty sides of 10 cadaveric heads were dissected and analyzed. The heads were divided into the following: Group A – narrow anterior incisura and Group B – wide anterior incisura – using 26.6 mm as a cutoff distance of the AIW. Subsequently, the area of the COT and the OCT in the t

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32

Xia, Jianguo. "Representations of Subgroups of Universal Triangle Groups." Algebra Colloquium 14, no. 02 (2007): 181–90. http://dx.doi.org/10.1142/s1005386707000181.

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Let G be a universal triangle group, and H a subgroup of G such that the chamber system ΔH is a tight triangle geometry. Then H, which is canonically isomorphic to the topological fundamental group π1(ΔH) of ΔH, is a finitely presented group. For some H we give their representations.

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33

Bényi, Árpád, and Branko Ćurgus. "Triangles and groups via cevians." Journal of Geometry 103, no. 3 (2012): 375–408. http://dx.doi.org/10.1007/s00022-013-0142-x.

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34

Tsanov, Valdemar. "Triangle groups, automorphic forms, and torus knots." L’Enseignement Mathématique 59, no. 1 (2013): 73–113. http://dx.doi.org/10.4171/lem/59-1-3.

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35

Bouw, Irene, and Martin Möller. "Teichmüller curves, triangle groups, and Lyapunov exponents." Annals of Mathematics 172, no. 1 (2010): 139–85. http://dx.doi.org/10.4007/annals.2010.172.139.

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36

Naud, Frédéric, Anke Pohl, and Louis Soares. "Fractal Weyl bounds and Hecke triangle groups." Electronic Research Announcements 26 (2019): 24–35. http://dx.doi.org/10.3934/era.2019.26.003.

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37

WILLIAMS, ALUN G. T. "Euler characteristics for orbifold generalized triangle groups." Mathematical Proceedings of the Cambridge Philosophical Society 132, no. 3 (2002): 435–38. http://dx.doi.org/10.1017/s030500410100562x.

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A generalized triangle group is a group with a presentationGT(l, m, n; w) = 〈a, b | al = bm = wn = 1〉;where l, m, n [ges ] 2, and w is a cyclically reduced word in the free product on {a, b}. In the setting of one-relator products of cyclic groups, Fine et al. [3] calculated their Euler characteristics for n [ges ] 3 under certain conditions on the defining word w.

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38

Maclachlan, C., and G. J. Martin. "The non-compact arithmetic generalised triangle groups." Topology 40, no. 5 (2001): 927–44. http://dx.doi.org/10.1016/s0040-9383(00)00003-3.

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39

Movasati, Hossein, and Khosro M. Shokri. "Automorphic forms for triangle groups: Integrality properties." Journal of Number Theory 145 (December 2014): 67–78. http://dx.doi.org/10.1016/j.jnt.2014.05.025.

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40

Conder, Marston D. E., and Gaven J. Martin. "Cusps, triangle groups and hyperbolic 3-folds." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 55, no. 2 (1993): 149–82. http://dx.doi.org/10.1017/s1446788700032018.

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AbstractWe provide a number of explicit examples of small volume hyperbolic 3-manifolds and 3-orbifolds with various geometric properties. These include a sequence of orbifolds with torsion of order q interpolating between the smallest volume cusped orbifold (q = 6) and the smallest volume limit orbifold (q → ∞), hyperbolic 3-manifolds with automorphism groups with large orders in relation to volume and in arithmetic progression, and the smallest volume hyperbolic manifolds with totally geodesic surfaces. In each case we provide a presentation for the associated Kleinian group and exhibit a fu

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41

Nugent, Steve, and John Voight. "On the arithmetic dimension of triangle groups." Mathematics of Computation 86, no. 306 (2016): 1979–2004. http://dx.doi.org/10.1090/mcom/3147.

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42

Fine, Benjamin, James Howie, and Gerhard Rosenberger. "Ree — Mendelsohn pairs in generalized triangle groups." Communications in Algebra 17, no. 2 (1989): 251–58. http://dx.doi.org/10.1080/00927878908823726.

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43

Mazhar, Siddiqua. "Composition of permutation representations of triangle groups." Communications in Algebra 48, no. 2 (2019): 792–802. http://dx.doi.org/10.1080/00927872.2019.1662911.

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44

Schwartz, Richard Evan. "Degenerating the complex hyperbolic ideal triangle groups." Acta Mathematica 186, no. 1 (2001): 105–54. http://dx.doi.org/10.1007/bf02392717.

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45

Jambor, Sebastian, Alastair Litterick, and Claude Marion. "On finite simple images of triangle groups." Israel Journal of Mathematics 227, no. 1 (2018): 131–62. http://dx.doi.org/10.1007/s11856-018-1722-0.

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46

Schmidt, Thomas A., and Mark Sheingorn. "Length spectra of the Hecke triangle groups." Mathematische Zeitschrift 220, no. 1 (1995): 369–97. http://dx.doi.org/10.1007/bf02572621.

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47

Edjvet, M. "On Certain Quotients of the Triangle Groups." Journal of Algebra 169, no. 2 (1994): 367–91. http://dx.doi.org/10.1006/jabr.1994.1290.

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48

Parker, John. "Unfaithful complex hyperbolic triangle groups, I: Involutions." Pacific Journal of Mathematics 238, no. 1 (2008): 145–69. http://dx.doi.org/10.2140/pjm.2008.238.145.

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49

Cao, Wensheng, and Xiaolin Huang. "A Note on Quaternionic Hyperbolic Ideal Triangle Groups." Canadian Mathematical Bulletin 59, no. 2 (2016): 244–57. http://dx.doi.org/10.4153/cmb-2015-084-2.

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AbstractIn this paper, the quaternionic hyperbolic ideal triangle groups are parametrized by a real one-parameter family {ϕ: s ∊ ℝ}. The indexing parameter s is the tangent of the quaternionic angular invariant of a triple of points in forming this ideal triangle. We show that if , then ϕs is not a discrete embedding, and if s , then ϕs is a discrete embedding.

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50

Friedman, Robert S. "American Nuclear Energy Policy, 1945–1990: A Review Essay." Journal of Policy History 3, no. 3 (1991): 331–48. http://dx.doi.org/10.1017/s0898030600006321.

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Political scientists have often referred to core decision-making groups in American politics as “policy communities” or, more popularly, as “the iron triangle.” Invariably, they are describing the interaction patterns of specialists in the executive and legislative branches of government and in the private sector who devote primary attention to the initiation and implementation of public policy in a particular issue area. In large measure the groups are depicted as having close-knit working relationships that result from frequent interaction, similarity in information sources and commonality i

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