AI Summary & Key Takeaways
AI InsightIf for a non-identity element x \in G, CG (x) is infinite then, CG (x) cannot contain H.
📌 3 Key Takeaways
Abstract
B. Hartley asked the following question: Does there exist a torsion free barely transitive group? Existence of torsion free simple barely transitive group is also unknown. We answer the latter question negatively in a special case. Moreover we proved the following: Let G be a simple barely transitive group, and H be a stabilizer of a point. If for a non-identity element x \in G, CG (x) is infinite then, CG (x) cannot contain H.
Özet
B. Hartley asked the following question: Does there exist a torsion free barely transitive group? Existence of torsion free simple barely transitive group is also unknown. We answer the latter question negatively in a special case. Moreover we proved the following: Let G be a simple barely transitive group, and H be a stabilizer of a point. If for a non-identity element x \in G, CG (x) is infinite then, CG (x) cannot contain H.