Minimal normal subgroups of transitive permutation groups of square-free degreeDobson, Edward Tauscher (Avtor) Malnič, Aleksander (Avtor) Marušič, Dragan (Avtor) Nowitz, Lewis A. (Avtor) mathematicsgraph theorytransitive permutation group2-closed groupsquare-free degreesemiregular automorphismvertex-transitive graphIt is shown that a minimal normal subgroup of a transitive permutation group of square-free degree in its induced action is simple and quasiprimitive, with three exceptions related to ▫$A_5$▫, ▫$A_7$▫, and PSL(2,29). Moreover, it is shown that a minimal normal subgroup of a 2-closed permutation group of square-free degree in its induced action is simple. As an almost immediate consequence, it follows that a 2-closed transitive permutation group of square-free degree contains a semiregular element of prime order, thus giving a partial affirmative answer to the conjecture that all 2-closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs,Discrete Math. 36 (1981) 69-81; P.J. Cameron (Ed.), Problems from the fifteenth British combinatorial conference, Discrete Math. 167/168 (1997) 605-615]).20072016-04-08 16:46:23Delo ni kategorizirano7719ISSN: 0012-365XUDK: 519.17:512.54OceCobissID: 1118479COBISS.SI-ID: 14179673sl