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="17.3709pt" id="M337" style="vertical-align:-5.934799pt" version="1.1" viewbox="-0.0498162 -11.4361 23.5831 17.3709" width="23.5831pt" 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="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.065,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.104,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.739,3.784)"><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,-0.0065,14.242,5.885)"><path d="M468 176V229H370V632H320C217 496 117 353 22 210V176H288V112C288 46 284 42 191 35V0H457V35C374 42 370 46 370 110V176H468ZM288 229H94C161 337 222 429 286 518H288V229Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.912,0)"><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

tab5

Table 5

Table 5: A Comprehensive Overview on the Formation of Homomorphic Copies in Coset Graphs for the Modular Group 