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Combinatorial group theory

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170: 142: 189: 56:, which today largely subsumes combinatorial group theory, using techniques from outside combinatorics besides. 165:, Studies in the History of Mathematics and Physical Sciences (1st ed.), Springer, p. 234, 60: 112:, in the early 1880s, who gave the first systematic study of groups by generators and relations. 64: 33: 29: 91: 53: 37: 134: 95: 52:
having in a natural and geometric way such a presentation. A very closely related topic is
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The History of Combinatorial Group Theory: A Case Study in the History of Ideas
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The foundations of combinatorial group theory were laid by
83:) for a detailed history of combinatorial group theory. 181: 156: 80: 122: 128: 101:via the edge graph of the dodecahedron. 182: 13: 86:A proto-form is found in the 1856 14: 201: 59:It also comprises a number of 1: 115: 7: 131:Mathematics and its history 63:problems, most notably the 10: 206: 190:Combinatorial group theory 81:Chandler & Magnus 1982 74: 22:combinatorial group theory 61:algorithmically insoluble 129:Stillwell, John (2002), 94:, where he studied the 65:word problem for groups 30:presentation of a group 28:, and the concept of a 92:William Rowan Hamilton 54:geometric group theory 40:. It is much used in 161:(December 1, 1982), 133:, Springer, p.  67:; and the classical 50:simplicial complex 42:geometric topology 172:978-0-387-90749-9 144:978-0-387-95336-6 46:fundamental group 24:is the theory of 197: 175: 148: 147: 126: 106:Walther von Dyck 88:icosian calculus 69:Burnside problem 205: 204: 200: 199: 198: 196: 195: 194: 180: 179: 178: 173: 159:Magnus, Wilhelm 152: 151: 145: 127: 123: 118: 77: 12: 11: 5: 203: 193: 192: 177: 176: 171: 157:Chandler, B.; 153: 150: 149: 143: 120: 119: 117: 114: 99:symmetry group 76: 73: 9: 6: 4: 3: 2: 202: 191: 188: 187: 185: 174: 168: 164: 160: 155: 154: 146: 140: 136: 132: 125: 121: 113: 111: 108:, student of 107: 102: 100: 97: 93: 89: 84: 82: 72: 70: 66: 62: 57: 55: 51: 47: 43: 39: 35: 31: 27: 23: 19: 162: 130: 124: 103: 85: 78: 58: 21: 15: 110:Felix Klein 96:icosahedral 26:free groups 18:mathematics 116:References 34:generators 38:relations 184:Category 75:History 169:  141:  44:, the 79:See ( 48:of a 167:ISBN 139:ISBN 36:and 135:374 90:of 32:by 16:In 186:: 137:, 71:. 20:,

Index

mathematics
free groups
presentation of a group
generators
relations
geometric topology
fundamental group
simplicial complex
geometric group theory
algorithmically insoluble
word problem for groups
Burnside problem
Chandler & Magnus 1982
icosian calculus
William Rowan Hamilton
icosahedral
symmetry group
Walther von Dyck
Felix Klein
374
ISBN
978-0-387-95336-6
Magnus, Wilhelm
ISBN
978-0-387-90749-9
Category
Combinatorial group theory

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