groups.g

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#W  globals.g               automgrp package                   Yevgen Muntyan
#W                                                             Dmytro Savchuk
##  automgrp v 1.3
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#Y  Copyright (C) 2003 - 2016 Yevgen Muntyan, Dmytro Savchuk
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##  AG_Groups
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##  This record contains the definitions of several groups.
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BindGlobal("AG_Groups", rec(
  GrigorchukGroup := AutomatonGroup("a = (1,2), b = (a, c), c = (a, d), d = (1, b)", false),
  UniversalGrigorchukGroup := AutomatonGroup("a=(1,4)(2,5)(3,6), b=(a,a,1,b,b,b), c=(a,1,a,c,c,c), d=(1,a,a,d,d,d)", false),
  Basilica := AutomatonGroup("u = (v, 1)(1,2), v = (u, 1)", false),
  Lamplighter := AutomatonGroup("a = (a, b)(1,2), b = (a, b)", false),
  AddingMachine := AutomatonGroup("t = (1, t)(1,2)", false),
  AleshinGroup := AutomatonGroup("a = (b, c)(1,2), b = (c, b)(1,2), c = (a, a)", false),
  Bellaterra := AutomatonGroup("a = (c, c)(1,2), b = (a, b), c = (b, a)", false),
  InfiniteDihedral := AutomatonGroup("a = (a, a)(1,2), b = (b, a)", false),
  SushchanskyGroup := AutomatonGroup("\
      A=(1,1,1)(1,2,3), A2=(1,1,1)(1,3,2), B=(r_1,q_1,A),\
      r_1=(r_2,A,1), r_2=(r_3,1,1), r_3=(r_4,1,1),\
      r_4=(r_5,A,1), r_5=(r_6,A2,1), r_6=(r_7,A,1),\
      r_7=(r_8,A,1), r_8=(r_9,A,1), r_9=(r_1,A2,1),\
      q_1=(q_2,1,1), q_2=(q_3,A,1), q_3=(q_1,A,1)", false),
  Hanoi3 := AutomatonGroup("a23 = (a23, 1, 1)(2,3), a13 = (1, a13, 1)(1,3), a12 = (1, 1, a12)(1,2)", false),
  Hanoi4 := AutomatonGroup([[1,1,1,1,()],[1,1,2,2,(1,2)],[1,3,1,3,(1,3)],[1,4,4,1,(1,4)],[5,1,1,5,(2,3)],[6,1,6,1,(2,4)],[7,7,1,1,(3,4)]],["1","a12","a13","a14","a23","a24","a34"], false),
  GuptaSidki3Group := SelfSimilarGroup("a = (1,2,3), b = (a, a^-1, b)", false),
  GuptaFabrikowskiGroup := AutomatonGroup([[1,1,1,()],[1,1,1,(1,2,3)],[2,1,3,()]],["1","a","b"], false),
  BartholdiGrigorchukGroup := AutomatonGroup([[1,1,1,()],[1,1,1,(1,2,3)],[2,2,3,()]],["1","a","b"], false),
  GrigorchukErschlerGroup := AutomatonGroup([[1,1,()],[1,1,(1,2)],[2,3,()],[2,5,()],[1,4,()]],["1","a","b","c","d"], false),
  BartholdiNonunifExponGroup := AutomatonGroup([ [1,1,1,1,1,1,1,()],\
            [1,1,1,1,1,1,1,(1,5)(3,7)],[1,1,1,1,1,1,1,(2,3)(6,7)],[1,1,1,1,1,1,1,(4,6)(5,7)],\
            [5,2,1,1,1,1,1,()],[6,3,1,1,1,1,1,()],[7,4,1,1,1,1,1,()]],\
            ["1","x","y","z","x1","y1","z1"], false),
  IMG_z2plusI := AutomatonGroup([[1,1,()],[1,1,(1,2)],[2,4,()],[3,1,()]],["1","a","b","c"], false),
  Airplane := AutomatonGroup([[1,1,()],[1,3,(1,2)],[1,4,()],[2,1,()]],["1","a","b","c"], false),
  Rabbit := AutomatonGroup([[1,1,()],[3,1,(1,2)],[1,4,()],[2,1,()]],["1","a","b","c"], false),
  TwoStateSemigroupOfIntermediateGrowth := AutomatonSemigroup([[1,1,(1,2)],[2,1,Transformation([2,2])]],["f0","f1"], false),\
  UniversalD_omega := AutomatonGroup("a=(1,2)(3,4),b=(a,c,a,c),c=(b,1,1,b)", false),\
));


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