Knowledge

Infinite conjugacy class property

Source 📝

185: 226: 147: 109: 51:
if and only if the group has the infinite conjugacy class property. It will then be, provided the group is nontrivial, of type
245: 250: 76:, every conjugacy class consists of only one element, so ICC groups are, in a way, as far from being abelian as possible. 48: 219: 44: 255: 212: 21: 143: 105: 104:, Encyclopedia of mathematics and its applications, vol. 79, Cambridge University Press, 135: 157: 125:
Popa, Sorin (2007), "Deformation and rigidity for group actions and von Neumann algebras",
153: 33: 196: 239: 73: 126: 99: 184: 62: 17: 66: 65:
of an infinite set that leave all but a finite subset of elements fixed, and
37: 192: 139: 101:
Banach Algebras and the General Theory of *-Algebras, Volume 2
58:, i.e. it will possess a unique, faithful, tracial state. 200: 128:International Congress of Mathematicians. Vol. I 220: 134:, Eur. Math. Soc., Zürich, pp. 445–477, 8: 36:of every group element but the identity is 227: 213: 93: 91: 89: 61:Examples of ICC groups are the group of 85: 7: 181: 179: 161:. See in particular p. 450: " 14: 26:infinite conjugacy class property 183: 1: 199:. You can help Knowledge by 98:Palmer, Theodore W. (2001), 272: 178: 45:von Neumann group algebra 195:-related article is a 246:Infinite group theory 169:factor iff Γ is ICC". 251:Properties of groups 24:is said to have the 69:on two generators. 208: 207: 149:978-3-03719-022-7 263: 229: 222: 215: 187: 180: 170: 160: 140:10.4171/022-1/18 133: 122: 116: 114: 95: 47:of a group is a 271: 270: 266: 265: 264: 262: 261: 260: 236: 235: 234: 233: 176: 174: 173: 168: 150: 131: 124: 123: 119: 112: 97: 96: 87: 82: 56: 34:conjugacy class 12: 11: 5: 269: 267: 259: 258: 253: 248: 238: 237: 232: 231: 224: 217: 209: 206: 205: 188: 172: 171: 166: 148: 117: 110: 84: 83: 81: 78: 74:abelian groups 54: 28:, or to be an 13: 10: 9: 6: 4: 3: 2: 268: 257: 256:Algebra stubs 254: 252: 249: 247: 244: 243: 241: 230: 225: 223: 218: 216: 211: 210: 204: 202: 198: 194: 189: 186: 182: 177: 164: 159: 155: 151: 145: 141: 137: 130: 129: 121: 118: 113: 111:9780521366380 107: 103: 102: 94: 92: 90: 86: 79: 77: 75: 70: 68: 64: 59: 57: 50: 46: 41: 39: 35: 31: 27: 23: 19: 201:expanding it 190: 175: 162: 127: 120: 100: 71: 63:permutations 60: 52: 42: 29: 25: 15: 67:free groups 18:mathematics 240:Categories 80:References 165:Γ is a II 32:, if the 30:ICC group 38:infinite 193:algebra 158:2334200 156:  146:  108:  49:factor 191:This 132:(PDF) 22:group 197:stub 144:ISBN 106:ISBN 43:The 20:, a 136:doi 72:In 16:In 242:: 154:MR 152:, 142:, 88:^ 53:II 40:. 228:e 221:t 214:v 203:. 167:1 163:L 138:: 115:. 55:1

Index

mathematics
group
conjugacy class
infinite
von Neumann group algebra
factor
permutations
free groups
abelian groups



Banach Algebras and the General Theory of *-Algebras, Volume 2
ISBN
9780521366380
International Congress of Mathematicians. Vol. I
doi
10.4171/022-1/18
ISBN
978-3-03719-022-7
MR
2334200
Stub icon
algebra
stub
expanding it
v
t
e
Categories

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.