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Non-simplicity of locally finite barely transitive groups

Published online by Cambridge University Press:  20 January 2009

B. Hartley  and
M. Kuzucuoğlu
B. Hartley
Affiliation:
Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey E-mail: [email protected]
M. Kuzucuoğlu
Affiliation:
Department of Mathematics, Middle East Technical University, 06531, Ankara, Turkey E-mail: [email protected]
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Abstract

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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 Ω so that G is a group of finitary permutations on Ω. 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′ ≅ Cp∞, and G′ is an abelian group of finite exponent.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 3 , October 1997 , pp. 483 - 490
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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