Number of Distinct Homomorphic Images in Coset Diagrams

<div>Homomorphic images <span class="nowrap"><svg height="18.5962pt" id="M874" style="vertical-align:-7.004801pt" version="1.1" viewbox="-0.0498162 -11.5914 26.0998 18.5962" width="26.0998pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.841,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.273,-5.741)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.841,3.784)"><path d="M238 675C244 702 241 710 231 710C220 710 155 682 74 673L70 643H101C147 643 151 635 142 594L39 111C18 11 36 -12 55 -12C89 -12 170 38 223 103L207 129C176 98 130 68 118 68C113 68 108 72 114 102L238 675Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,12.08,5.885)"><path d="M318 -137C221 -59 159 100 159 272S220 600 318 680L294 710C146 612 80 452 80 273V272C80 91 146 -72 294 -168L318 -137Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,14.485,5.885)"><path d="M436 222C436 297 385 359 295 376V378C320 391 343 407 363 428S394 474 394 501C394 578 333 635 239 635C186 635 138 610 110 577L63 514L91 490C114 525 158 571 211 571C266 571 306 541 306 483C306 411 234 371 141 343L151 306C167 311 192 317 219 317C276 317 344 282 344 194C346 102 296 46 227 46C166 46 125 76 99 97C91 104 81 103 71 97C62 90 47 75 46 62C44 50 48 39 62 26C77 10 120 -12 168 -12C242 -12 436 62 436 222Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,17.696,5.885)"><path d="M202 22C202 97 141 138 100 138C74 138 46 121 46 92C46 74 56 66 61 64C97 55 127 31 127 -5C127 -43 97 -68 44 -90L59 -129C127 -110 202 -64 202 22Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,19.295,5.885)"><path d="M436 222C436 297 385 359 295 376V378C320 391 343 407 363 428S394 474 394 501C394 578 333 635 239 635C186 635 138 610 110 577L63 514L91 490C114 525 158 571 211 571C266 571 306 541 306 483C306 411 234 371 141 343L151 306C167 311 192 317 219 317C276 317 344 282 344 194C346 102 296 46 227 46C166 46 125 76 99 97C91 104 81 103 71 97C62 90 47 75 46 62C44 50 48 39 62 26C77 10 120 -12 168 -12C242 -12 436 62 436 222Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,22.506,5.885)"><path d="M291 272C291 452 228 611 76 710L51 680C147 602 211 444 211 272S151 -55 51 -137L76 -168C227 -66 291 91 291 272Z"></path></g></svg>.</span></div>

Journal of Mathematics

Number of Distinct Homomorphic Images in Coset Diagrams

Figure 29