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Non-simplicity of locally finite barely transitive groups
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Date
1997-10-01
Author
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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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.