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McKay conjecture

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283: 458: 319: 497: 163: 572: 537: 517: 343: 183: 137: 117: 83: 57: 191: 613: 351: 559: 88: 60: 291: 581: 555: 466: 142: 591: 322: 33: 278:{\displaystyle {\textrm {Irr}}_{p'}(G):=\{\chi \in {\textrm {Irr}}(G):p\nmid \chi (1)\}} 522: 502: 328: 168: 122: 102: 68: 64: 42: 607: 37: 21: 17: 29: 570:
Evseev, Anton (2013). "The McKay Conjecture and Brauer's Induction Theorem".
595: 453:{\displaystyle |{\textrm {Irr}}_{p'}(G)|=|{\textrm {Irr}}_{p'}(N_{G}(P))|} 566:(Corrected reprint of the 1976 original, published by Academic Press.) 586: 32:
of equality between the number of irreducible complex
525: 505: 469: 354: 331: 294: 194: 171: 145: 125: 105: 71: 45: 531: 511: 491: 452: 337: 313: 277: 177: 157: 131: 111: 77: 51: 573:Proceedings of the London Mathematical Society 8: 272: 226: 87:. It is named after Canadian mathematician 345:. The McKay conjecture claims the equality 585: 524: 504: 474: 468: 445: 427: 409: 403: 402: 396: 388: 368: 362: 361: 355: 353: 330: 296: 295: 293: 236: 235: 203: 197: 196: 193: 170: 144: 124: 104: 70: 44: 7: 314:{\displaystyle {\textrm {Irr}}(G)} 14: 552:Character Theory of Finite Groups 614:Representation theory of groups 20:, specifically in the field of 486: 480: 446: 442: 439: 433: 420: 397: 389: 385: 379: 356: 308: 302: 269: 263: 248: 242: 220: 214: 1: 36:of degree not divisible by a 321:denotes the set of complex 630: 492:{\displaystyle N_{G}(P)} 158:{\displaystyle P\leq G} 139:is a finite group, and 533: 513: 493: 454: 339: 323:irreducible characters 315: 279: 179: 159: 133: 113: 79: 53: 550:Isaacs, I.M. (1994). 534: 514: 499:is the normalizer of 494: 455: 340: 316: 280: 180: 160: 134: 114: 80: 54: 523: 503: 467: 352: 329: 292: 192: 169: 143: 123: 103: 69: 43: 596:10.1112/plms/pds058 119:is a prime number, 529: 509: 489: 450: 335: 311: 275: 185:-subgroup. Define 175: 155: 129: 109: 75: 49: 532:{\displaystyle G} 512:{\displaystyle P} 406: 365: 338:{\displaystyle G} 299: 239: 200: 178:{\displaystyle p} 132:{\displaystyle G} 112:{\displaystyle p} 78:{\displaystyle p} 52:{\displaystyle p} 26:McKay conjecture 621: 599: 589: 565: 538: 536: 535: 530: 518: 516: 515: 510: 498: 496: 495: 490: 479: 478: 459: 457: 456: 451: 449: 432: 431: 419: 418: 417: 408: 407: 404: 400: 392: 378: 377: 376: 367: 366: 363: 359: 344: 342: 341: 336: 320: 318: 317: 312: 301: 300: 297: 284: 282: 281: 276: 241: 240: 237: 213: 212: 211: 202: 201: 198: 184: 182: 181: 176: 164: 162: 161: 156: 138: 136: 135: 130: 118: 116: 115: 110: 84: 82: 81: 76: 58: 56: 55: 50: 629: 628: 624: 623: 622: 620: 619: 618: 604: 603: 602: 569: 562: 549: 545: 521: 520: 501: 500: 470: 465: 464: 423: 410: 401: 369: 360: 350: 349: 327: 326: 290: 289: 204: 195: 190: 189: 167: 166: 141: 140: 121: 120: 101: 100: 97: 67: 66: 59:to that of the 41: 40: 12: 11: 5: 627: 625: 617: 616: 606: 605: 601: 600: 567: 560: 546: 544: 541: 528: 508: 488: 485: 482: 477: 473: 461: 460: 448: 444: 441: 438: 435: 430: 426: 422: 416: 413: 399: 395: 391: 387: 384: 381: 375: 372: 358: 334: 310: 307: 304: 286: 285: 274: 271: 268: 265: 262: 259: 256: 253: 250: 247: 244: 234: 231: 228: 225: 222: 219: 216: 210: 207: 174: 154: 151: 148: 128: 108: 96: 93: 74: 48: 13: 10: 9: 6: 4: 3: 2: 626: 615: 612: 611: 609: 597: 593: 588: 583: 580:: 1248–1290. 579: 575: 574: 568: 563: 561:0-486-68014-2 557: 553: 548: 547: 542: 540: 526: 506: 483: 475: 471: 436: 428: 424: 414: 411: 393: 382: 373: 370: 348: 347: 346: 332: 325:of the group 324: 305: 266: 260: 257: 254: 251: 245: 232: 229: 223: 217: 208: 205: 188: 187: 186: 172: 152: 149: 146: 126: 106: 94: 92: 90: 86: 72: 62: 46: 39: 35: 31: 27: 23: 19: 577: 571: 551: 462: 287: 98: 38:prime number 25: 22:group theory 15: 165:is a Sylow 18:mathematics 543:References 89:John McKay 61:normalizer 34:characters 30:conjecture 587:1009.1413 554:. Dover. 261:χ 258:∤ 233:∈ 230:χ 150:≤ 95:Statement 85:-subgroup 608:Category 415:′ 374:′ 209:′ 99:Suppose 558:  463:where 288:where 65:Sylow 24:, the 582:arXiv 63:of a 28:is a 556:ISBN 592:doi 578:106 519:in 405:Irr 364:Irr 298:Irr 238:Irr 199:Irr 16:In 610:: 590:. 576:. 539:. 224::= 91:. 598:. 594:: 584:: 564:. 527:G 507:P 487:) 484:P 481:( 476:G 472:N 447:| 443:) 440:) 437:P 434:( 429:G 425:N 421:( 412:p 398:| 394:= 390:| 386:) 383:G 380:( 371:p 357:| 333:G 309:) 306:G 303:( 273:} 270:) 267:1 264:( 255:p 252:: 249:) 246:G 243:( 227:{ 221:) 218:G 215:( 206:p 173:p 153:G 147:P 127:G 107:p 73:p 47:p

Index

mathematics
group theory
conjecture
characters
prime number
normalizer
Sylow p {\displaystyle p} -subgroup
John McKay
irreducible characters
ISBN
0-486-68014-2
Proceedings of the London Mathematical Society
arXiv
1009.1413
doi
10.1112/plms/pds058
Category
Representation theory of groups

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