On groups with every normal subgroup transitive or semiregular.

DOI10.1016/j.jalgebra.2007.10.014zbMath1147.20004OpenAlexW2037415122MaRDI QIDQ2482076

Áron Bereczky, Attila Maróti

Publication date: 16 April 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2007.10.014

zbMATH Keywords

Frobenius groupsCoxeter groupsnormal subgroupsprimitive permutation groupsfinite permutation groupskernelsuniversal algebraregular permutation groupsinnately transitive permutation groupsquasiprimitive permutation groupssolvable permutation groupssemiprimitive permutation groupscollapsing monoids

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Structure theory of algebraic structures (08A05) Primitive groups (20B15) General theory for finite permutation groups (20B05) Characterization theorems for permutation groups (20B10)

Related Items (10)

Two local conditions on the vertex stabiliser of arc-transitive graphs and their effect on the Sylow subgroups ⋮ A theory of semiprimitive groups ⋮ A class of semiprimitive groups that are graph-restrictive ⋮ Bounding the size of a vertex-stabiliser in a finite vertex-transitive graph ⋮ On graph-restrictive permutation groups ⋮ On orders of automorphisms of vertex-transitive graphs ⋮ Vertex-transitive graphs with local action the symmetric group on ordered pairs ⋮ Bounds for finite semiprimitive permutation groups: order, base size, and minimal degree ⋮ On locally semiprimitive graphs and a theorem of Weiss ⋮ The distinguishing number of quasiprimitive and semiprimitive groups

Cites Work

• Unary polynomials in algebras. I
• An O'Nan-Scott Theorem for Finite Quasiprimitive Permutation Groups and an Application to 2-Arc Transitive Graphs
• Simplicity condition for the fundamental ideal of the modular group algebra of a locally finite group
• Finite permutation groups with a transitive minimal normal subgroup
• Collapsing permutation groups.
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