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2. Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphismsDragan Marušič, 2017, izvirni znanstveni članek Opis: It has been conjectured that automorphism groups of vertex-transitive (di)graphs, and more generally 2-closures of transitive permutation groups, must necessarily possess a fixed-point-free element of prime order, and thus a non-identity element with all orbits of the same length, in other words, a semiregular element. The known affirmative answers for graphs with primitive and quasiprimitive groups of automorphisms suggest that solvable groups need to be considered if one is to hope for a complete solution of this conjecture. It is the purpose of this paper to present an overview of known results and suggest possible further lines of research towards a complete solution of the problem. Ključne besede: solvable group, semiregular automorphism, fixed-point-free automorphism, polycirculant conjecture Objavljeno v RUP: 03.01.2022; Ogledov: 893; Prenosov: 17 Celotno besedilo (235,26 KB) |
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5. Quasi-semiregular automorphisms of cubic and tetravalent arc-transitive graphs : Group Action and Combinatorial Structures, Nankai University, Tianjin, China, 15. - 18. 6. 2018István Kovács, Yan-Quan Feng, Ademir Hujdurović, Klavdija Kutnar, Dragan Marušič, 2018, prispevek na konferenci brez natisa Ključne besede: quasi-semiregular automorphism, cubic graph, tetravalent graph, arc-transitive graph Objavljeno v RUP: 06.12.2018; Ogledov: 2057; Prenosov: 129 Povezava na celotno besedilo |
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10. Minimal normal subgroups of transitive permutation groups of square-free degreeEdward Dobson, Aleksander Malnič, Dragan Marušič, Lewis A. Nowitz, 2007, izvirni znanstveni članek Opis: 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]). Ključne besede: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph Objavljeno v RUP: 03.04.2017; Ogledov: 2442; Prenosov: 89 Povezava na celotno besedilo |