J. Aust. Math. Soc.
74 (2003), 267-285
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Strange permutation representations of free groups
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Meenaxi Bhattacharjee
Department of Mathematics
Indian Institute of Technology Guwahati
Guwahati
Assam 781039
India
meenaxi@iitg.ernet.in
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Abstract
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Certain permutation representations of free
groups are constructed by finite approximation.
The first is a construction of a cofinitary
group with special properties, answering a
question of Tim Wall published by Cameron. The
second yields, via a method of Kepert and Willis,
a totally disconnected locally compact group
which is compactly generated and uniscalar but
has no compact open normal subgroup. Finally, an
oligomorphic group of automorphisms of the random
graph is built, all of whose non-trivial
subgroups have just finitely many orbits.
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