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Barely transitive groups
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Date
2007
Author
Betin, Cansu
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A group G is called a barely transitive group if it acts transitively and faithfully on an infinite set and every orbit of every proper subgroup is finite. A subgroup H of a group G is called a permutable subgroup, if H commutes with every subgroup of G. We showed that if an infinitely generated barely transitive group G has a permutable point stabilizer, then G is locally finite. We proved that if a barely transitive group G has an abelian point stabilizer H, then G is isomorphic to one of the followings: (i) G is a metabelian locally finite p-group, (ii) G is a finitely generated quasi-finite group (in particular H is finite), (iii) G is a finitely generated group with a maximal normal subgroup N where N is a locally finite metabelian group. In particular, G=N is a quasi-finite simple group. In all of the three cases, G is periodic.
Subject Keywords
Permutation groups.
,
Algebra.
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http://etd.lib.metu.edu.tr/upload/3/12608605/index.pdf
https://hdl.handle.net/11511/17247
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Graduate School of Natural and Applied Sciences, Thesis
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C. Betin, “Barely transitive groups,” Ph.D. - Doctoral Program, Middle East Technical University, 2007.