Non-simplicity of locally finite barely transitive groups

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1997-10-01

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Hartley, B
Kuzucuoğlu, Mahmut

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We answer the following questions negatively: Does there exist a simple locally finite barely transitive group (LFBT-group)? More precisely we have: There exists no simple LFBT-group. We also deal with the question, whether there exists a LFBT-group G acting on an infinite set Omega so that G is a group of finitary permutations on Omega. Along this direction we prove: If there exists a finitary LFBT-group G, then G is a minimal non-FC p-group. Moreover we prove that: If a stabilizer of a point in a LFBT-group G is abelian, then G is metabelian. Furthermore G is a p-group for some prime p, G/G' congruent to C-p infinity and G' is an abelian group of finite exponent.

Subject Keywords

General Mathematics

URI

https://hdl.handle.net/11511/41081

Journal

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY

DOI

https://doi.org/10.1017/s0013091500023968

Collections

Department of Mathematics, Article

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Citation Formats

B. Hartley and M. Kuzucuoğlu, “Non-simplicity of locally finite barely transitive groups,” PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, pp. 483–490, 1997, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41081.