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Strange permutation representations of free groups

Part of: Permutation groups

Published online by Cambridge University Press:  09 April 2009

Meenaxi Bhattacharjee  and
Dugald MacPherson
Meenaxi Bhattacharjee
Affiliation:
Department of Mathematics Indian Institute of Technology GuwahatiGuwahati Assam 781039India e-mail: [email protected]
Dugald MacPherson
Affiliation:
Department of Pure Mathematics University of LeedsLeeds LS2 9JTEngland e-mail: [email protected]
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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.

MSC classification

Secondary: 20B07: General theory for infinite groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 267 - 286
Copyright
Copyright © Australian Mathematical Society 2003

References

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