Graphical Frobenius representations of non-abelian groups
Korchmáros, Gábor ; Nagy, Gábor Péter, 1972-
Grupa ▫$G$▫ ima Frobeniusovo grafovsko predstavitev, če obstaja enostaven graf ▫$\Gamma$▫, katerega polna grupa avtomorfizmov je izomorfna grupi ▫$G$▫, ki deluje na vozliščih kot Frobeniusova grupa. ...Vsaka grupa ▫$G$▫, ki ima takšno predstavitev, je Frobeniusova grupa in ▫$\Gamma$▫ je Cayleyjev graf. Po nedavnih rezultatih Spige, obstaja funkcija ▫$f$▫, za katero velja, da če je ▫$G$▫ končna Frobeniusova grupa s komplementom ▫$H$▫ in je ▫$|G| > f(|H|)$▫, potem ▫$G$▫ dopušča Frobeniusovo grafovsko predstavitev. V tem predstavimo neskončno družino grafov, ki dopuščajo Frobeniusovo grafovsko predstavitev, čeprav ne ustrezajo Spigovi meji. V naši konstrukciji je grupa ▫$G$▫ Higmanova grupa ▫$A(f, q_0)$▫ za neskončno zaporedje funkcij ▫$f$▫ in ▫$q_0$▫, ki ima nekomutativno jedro ter komplement lihega reda.
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