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1.
Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphisms
Dragan Marušič, 2017, original scientific article

Abstract: 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.
Keywords: solvable group, semiregular automorphism, fixed-point-free automorphism, polycirculant conjecture
Published in RUP: 03.01.2022; Views: 776; Downloads: 17
.pdf Full text (235,26 KB)

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Symmetric graphs: why semiregularity matters
Dragan Marušič, 2018, published scientific conference contribution abstract (invited lecture)

Keywords: vertex-transitive graph, semiregular automorphism, elusive group, solvable group
Published in RUP: 07.02.2018; Views: 1974; Downloads: 28
URL Link to full text

4.
A note on finite non-solvable groups with few non-cyclic subgroups
Jiangtao Shi, Cui Zhang, 2011, original scientific article

Keywords: finite group, non-cyclic subgroup, non-solvable group
Published in RUP: 15.10.2013; Views: 2877; Downloads: 44
URL Link to full text

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