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AI InsightIf for a non-identity element x \in G, CG (x) is infinite then, CG (x) cannot contain H.
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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.
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.