Number of Distinct Homomorphic Images in Coset Diagrams

<div>Homomorphic images <span class="nowrap"><svg height="18.5962pt" id="M362" 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="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></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="M452 139L416 148C386 81 373 77 319 77H141L282 220C372 312 414 373 414 464C414 569 332 635 240 635C181 635 132 609 101 574L42 493L70 467C98 506 143 562 209 562C280 562 324 515 324 435C324 347 261 272 197 197C148 139 89 84 34 29V0H417L452 139Z"></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 7