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Title: Minimal normal subgroups of transitive permutation groups of square-free degree Malnič, Aleksander (Author)Marušič, Dragan (Author)Dobson, Edward (Author)Nowitz, Lewis A. (Author) http://dx.doi.org/10.1016/j.disc.2005.09.029 English Not categorized 1.01 - Original Scientific Article IAM - Andrej Marušič Institute It 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]). mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph 2007 str. 373-385 Vol. 307, iss. 3-5 0012-365X 519.17:512.54 14179673 1041 58 Document is not linked to any category.

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## Secondary language

Language: English matematika, teorija grafov, tranzitivna permutacijska grupa, 2-zaprta grupa, polregularni avtomorfizem, točkovno tranzitivni grafi