N-barely transitive permutation groups
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DOI: 10.1007/s11587-021-00608-x
Abstract: A group G is an N-barely transitive group (NBT-group) if G acts on an infinite set transitively and faithfully and all proper normal subgroups of G have finite orbits. We investigate the main properties and… read more here.
Keywords: transitive permutation; permutation groups; barely transitive; group ... See more keywords
Group factorisations, uniform automorphisms, and permutation groups of simple diagonal type
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DOI: 10.1007/s11856-018-1790-1
Abstract: We present a new proof, which is independent of the finite simple group classification and applies also to infinite groups, that quasiprimitive permutation groups of simple diagonal type cannot be embedded into wreath products in… read more here.
Keywords: permutation groups; group; groups simple; diagonal type ... See more keywords
Characters of finite permutation groups and Krein parameters
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DOI: 10.1016/j.jalgebra.2018.07.039
Abstract: Abstract Let G be a transitive permutation group on a finite set Ω. If G is multiplicity-free, then End G ( C [ Ω ] ) is commutative, and Krein parameters q i , j… read more here.
Keywords: finite permutation; characters finite; permutation groups; permutation ... See more keywords
Finite quasiprimitive permutation groups with a metacyclic transitive subgroup
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DOI: 10.1016/j.jalgebra.2021.08.023
Abstract: In this paper, we classify finite quasiprimitive permutation groups with a metacyclic transitive subgroup, solving a problem initiated by Wielandt in 1949. It also involves the classification of factorizations of almost simple groups with a… read more here.
Keywords: permutation groups; quasiprimitive permutation; transitive subgroup; groups metacyclic ... See more keywords
Bounds for finite semiprimitive permutation groups: order, base size, and minimal degree
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DOI: 10.1017/s0013091520000346
Abstract: Abstract In this paper, we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. These groups have recently been investigated in terms of their abstract structure, in… read more here.
Keywords: order base; base size; semiprimitive permutation; finite semiprimitive ... See more keywords
Finite permutation groups with few orbits under the action on the power set
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DOI: 10.1216/rmj.2021.51.1553
Abstract: We study the orbits under the natural action of a permutation group $G \subseteq S_n$ on the powerset $\mathscr{P}(\{1, \dots , n\})$. The permutation groups having exactly $n+1$ orbits on the powerset can be characterized… read more here.
Keywords: orbits action; finite permutation; permutation groups; groups orbits ... See more keywords
Remarks on Hopf Images and Quantum Permutation Groups $S_{n}^{+}$
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DOI: 10.4153/cmb-2017-028-2
Abstract: Abstract Motivated by a question of A. Skalski and P. M. Sołtan (2016) about inner faithfulness of S. Curran’s map of extending a quantum increasing sequence to a quantum permutation, we revisit the results and… read more here.
Keywords: permutation groups; permutation; quantum permutation; images quantum ... See more keywords