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Triple product property

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448: 362: 222: 185: 148: 87: 405: 385: 111: 49: 489: 411: 230: 482: 447: 513: 518: 475: 508: 54: 25: 424: 190: 153: 116: 17: 459: 390: 370: 96: 34: 502: 455: 435:, 11–14 October 2003, Cambridge, MA, IEEE Computer Society, pp. 438–449. 423:
Henry Cohn, Chris Umans. A Group-theoretic Approach to Fast Matrix Multiplication.
433:
Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
428: 357:{\displaystyle s's^{-1}t't^{-1}u'u^{-1}=1\Rightarrow s'=s,t'=t,u'=u} 463: 393: 373: 233: 193: 156: 119: 99: 57: 37: 399: 379: 356: 216: 179: 142: 105: 81: 43: 51:be a non-trivial group. Three nonempty subsets 483: 8: 490: 476: 392: 372: 288: 267: 246: 232: 192: 155: 118: 98: 56: 36: 412:fast matrix multiplication algorithms 7: 444: 442: 14: 24:is an identity satisfied in some 446: 410:It plays a role in research of 303: 82:{\displaystyle S,T,U\subset G} 1: 462:. You can help Knowledge by 535: 441: 217:{\displaystyle u,u'\in U} 180:{\displaystyle t,t'\in T} 143:{\displaystyle s,s'\in S} 91:triple product property 22:triple product property 458:-related article is a 401: 381: 358: 218: 181: 144: 107: 83: 45: 402: 382: 359: 219: 182: 145: 108: 89:are said to have the 84: 46: 514:Properties of groups 391: 371: 231: 224:it is the case that 191: 154: 117: 113:if for all elements 97: 55: 35: 387:is the identity of 519:Group theory stubs 397: 377: 354: 214: 177: 140: 103: 79: 41: 471: 470: 400:{\displaystyle G} 380:{\displaystyle 1} 106:{\displaystyle G} 44:{\displaystyle G} 526: 492: 485: 478: 450: 443: 406: 404: 403: 398: 386: 384: 383: 378: 363: 361: 360: 355: 347: 330: 313: 296: 295: 283: 275: 274: 262: 254: 253: 241: 223: 221: 220: 215: 207: 186: 184: 183: 178: 170: 149: 147: 146: 141: 133: 112: 110: 109: 104: 88: 86: 85: 80: 50: 48: 47: 42: 18:abstract algebra 534: 533: 529: 528: 527: 525: 524: 523: 499: 498: 497: 496: 439: 429:math.GR/0307321 420: 389: 388: 369: 368: 340: 323: 306: 284: 276: 263: 255: 242: 234: 229: 228: 200: 189: 188: 163: 152: 151: 126: 115: 114: 95: 94: 53: 52: 33: 32: 12: 11: 5: 532: 530: 522: 521: 516: 511: 501: 500: 495: 494: 487: 480: 472: 469: 468: 451: 437: 436: 419: 416: 396: 376: 365: 364: 353: 350: 346: 343: 339: 336: 333: 329: 326: 322: 319: 316: 312: 309: 305: 302: 299: 294: 291: 287: 282: 279: 273: 270: 266: 261: 258: 252: 249: 245: 240: 237: 213: 210: 206: 203: 199: 196: 176: 173: 169: 166: 162: 159: 139: 136: 132: 129: 125: 122: 102: 78: 75: 72: 69: 66: 63: 60: 40: 13: 10: 9: 6: 4: 3: 2: 531: 520: 517: 515: 512: 510: 509:Finite groups 507: 506: 504: 493: 488: 486: 481: 479: 474: 473: 467: 465: 461: 457: 452: 449: 445: 440: 434: 430: 426: 422: 421: 417: 415: 413: 408: 394: 374: 351: 348: 344: 341: 337: 334: 331: 327: 324: 320: 317: 314: 310: 307: 300: 297: 292: 289: 285: 280: 277: 271: 268: 264: 259: 256: 250: 247: 243: 238: 235: 227: 226: 225: 211: 208: 204: 201: 197: 194: 174: 171: 167: 164: 160: 157: 137: 134: 130: 127: 123: 120: 100: 92: 76: 73: 70: 67: 64: 61: 58: 38: 29: 27: 23: 19: 464:expanding it 456:group theory 453: 438: 432: 409: 366: 90: 30: 21: 15: 503:Categories 418:References 304:⇒ 290:− 269:− 248:− 209:∈ 172:∈ 135:∈ 74:⊂ 345:′ 328:′ 311:′ 281:′ 260:′ 239:′ 205:′ 168:′ 131:′ 367:where 26:groups 20:, the 454:This 425:arXiv 460:stub 31:Let 93:in 16:In 505:: 431:. 414:. 407:. 187:, 150:, 28:. 491:e 484:t 477:v 466:. 427:: 395:G 375:1 352:u 349:= 342:u 338:, 335:t 332:= 325:t 321:, 318:s 315:= 308:s 301:1 298:= 293:1 286:u 278:u 272:1 265:t 257:t 251:1 244:s 236:s 212:U 202:u 198:, 195:u 175:T 165:t 161:, 158:t 138:S 128:s 124:, 121:s 101:G 77:G 71:U 68:, 65:T 62:, 59:S 39:G

Index

abstract algebra
groups
fast matrix multiplication algorithms
arXiv
math.GR/0307321
Stub icon
group theory
stub
expanding it
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t
e
Categories
Finite groups
Properties of groups
Group theory stubs

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