N-barely transitive permutation groups

Alkis O., ARIKAN A., ARIKAN A.

RICERCHE DI MATEMATICA, vol.72, no.1, pp.141-152, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1007/s11587-021-00608-x
  • Journal Name: RICERCHE DI MATEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.141-152
  • Keywords: Barely transitive group, N-barely transitive group, Minimal non-FC-group, Finitary permutation group, Cofinitary permutation group, Perfect group, Locally soluble group
  • Gazi University Affiliated: Yes

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 structure of NBT-groups. We give some examples in non-perfect and perfect case. Also we show that there does not exist a locally soluble perfect cofinitary NBT-group.