Minimal normal subgroups of transitive permutation groups of square-free degree

DOI10.1016/j.disc.2005.09.029zbMath1110.05043OpenAlexW2026146987MaRDI QIDQ864124

Edward Dobson, Lewis A. Nowitz, Dragan Marušič, Aleksander Malnič

Publication date: 13 February 2007

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2005.09.029

zbMATH Keywords

vertex-transitive graphsemiregular automorphism2-closed groupsquare-free degree

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Subgroups of symmetric groups (20B35)

Related Items (22)

Cayley numbers with arbitrarily many distinct prime factors ⋮ Symmetry structure of bicirculants ⋮ Cubic arc-transitive \(k\)-multicirculants ⋮ Semiregular elements in transitive 2-closed permutation groups of certain degrees ⋮ All vertex-transitive locally-quasiprimitive graphs have a semiregular automorphism ⋮ Semiregular automorphisms of vertex-transitive graphs of certain valencies ⋮ Semiregular automorphisms of arc-transitive graphs with valency \(pq\) ⋮ Hamilton paths in vertex-transitive graphs of order \(10p\) ⋮ Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphisms ⋮ On Semiregular Elements of Solvable Groups ⋮ On 2-closed elusive permutation groups of degrees p2q and p2qr ⋮ On color-preserving automorphisms of Cayley graphs of odd square-free order ⋮ Semiregular automorphisms in vertex-transitive graphs of order \(3p^2\) ⋮ Quasi-semiregular automorphisms of cubic and tetravalent arc-transitive graphs ⋮ Vertex-transitive expansions of (1, 3)-trees ⋮ Characterizing a family of elusive permutation groups ⋮ On Elusive Permutation Groups of Square-Free Degree ⋮ Distance-transitive graphs admit semiregular automorphisms ⋮ Hamilton paths and cycles in vertex-transitive graphs of order \(6p\) ⋮ Hamilton cycles and paths in vertex-transitive graphs-current directions ⋮ On normality of \(n\)-Cayley graphs ⋮ Transitive group actions: (im)primitivity and semiregular subgroups.

Cites Work

• Imprimitive representations of \(SL(2,2^ k)\)
• On vertex symmetric digraphs
• Permutation groups, vertex-transitive digraphs and semiregular automorphisms
• Vertex-primitive graphs of order a product of two distinct primes
• On vertex-transitive, non-Cayley graphs of order \(pqr\)
• On solvable groups and circulant graphs
• On non-Cayley vertex-transitive graphs of order a product of three primes
• Isomorphism problem for Cayley graphs of \(\mathbb{Z}^ 3_ p\)
• Transitive Permutation Groups Without Semiregular Subgroups
• Characterizing vertex-transitivepq-graphs with an imprimitive automorphism subgroup
• THE PRIMITIVE PERMUTATION GROUPS OF SQUAREFREE DEGREE
• QUASIPRIMITIVE GROUPS WITH NO FIXED POINT FREE ELEMENTS OF PRIME ORDER
• Vertex-primitive groups and graphs of order twice the product of two distinct odd primes
• Vertex-transitive graphs that are not Cayley graphs. II
• Research problems
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