A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group

<div>Necessary information regarding homomorphic copies <span class="nowrap"><svg height="17.4296pt" id="M451" style="vertical-align:-5.9935pt" version="1.1" viewbox="-0.0498162 -11.4361 21.5759 17.4296" width="21.5759pt" 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="M293 -169V-141C218 -131 209 -90 209 -44C209 19 222 85 222 152C222 207 198 255 139 269V273C199 286 222 334 222 388C222 454 209 523 209 588C209 632 218 671 293 681V709C234 709 148 695 148 577C147 513 155 438 155 372C155 337 152 291 64 285V256C152 250 155 204 155 169C156 105 148 31 148 -41C148 -157 234 -169 293 -169Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.511,0)"><path d="M478 372C478 418 458 448 431 448C409 448 389 431 389 410C389 404 391 400 394 395C398 388 406 371 406 348C406 253 308 122 251 51H249C254 122 249 257 231 336C212 421 189 448 159 448C126 448 75 412 23 327L48 306C83 354 103 371 115 371C125 371 134 360 144 334C185 224 192 64 183 -19C146 -100 116 -202 110 -244L125 -261C154 -259 208 -234 222 -220C222 -194 225 -84 235 -23C247 -3 273 36 308 79C379 165 478 288 478 372Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.027,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.179,3.784)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,12.682,5.885)"><path d="M449 167C449 258 386 306 319 343C359 372 385 398 393 407C411 429 423 458 423 487C423 569 352 635 256 635C143 635 72 555 72 471C72 401 112 353 177 316C145 294 106 265 92 252C72 231 47 202 47 157C47 50 134 -12 245 -12C334 -12 449 50 449 167ZM342 480C342 424 315 389 281 362C208 395 150 428 150 498C150 546 184 597 242 597C290 597 342 559 342 480ZM365 143C365 72 316 26 255 26C193 26 133 76 133 163C133 216 166 264 216 296C294 259 365 217 365 143Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.91,0)"><path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z"></path></g></svg>.</span></div>

Journal of Mathematics

tab11

Table 11

Table 11: A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group 