Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T21:01:22.007Z Has data issue: false hasContentIssue false
  • English
  • Français

THE FIRST-ORDER THEORY OF BRANCH GROUPS

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  10 February 2016

JOHN S. WILSON
JOHN S. WILSON*
Affiliation:
Mathematical Institute, Oxford OX2 6GG, UK email John.Wilson@maths.ox.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that for many branch groups $G$ the action on the ambient tree can be interpreted in $G$ , in the sense of first-order model theory.

Keywords

branch grouprooted treeinterpretation

MSC classification

Primary: 20E08: Groups acting on trees
Secondary: 20E26: Residual properties and generalizations; residually finite groups 20F10: Word problems, other decision problems, connections with logic and automata
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 1 , February 2017 , pp. 150 - 158
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Abért, M., ‘Group laws and free subgroups in topological groups’, Bull. Lond. Math. Soc. 37 (2005), 525–534.Google Scholar
Bartholdi, L., Grigorchuk, R. I. and Sunik, Z., ‘Branch groups’, in: Handbook of Algebra, Vol. 3 (North-Holland, Amsterdam, 2003), 989–1112.Google Scholar
Borovik, A. and Nesin, A., Groups of Finite Morley Rank (Clarendon Press, Oxford, 1994).Google Scholar
Garrido, A., ‘On the congruence subgroup problem for branch groups’, Israel J. Math. to appear;arXiv:1405.3237.Google Scholar
Grigorchuk, R. I., ‘Just infinite branch groups’, in: New Horizons in Pro-p Groups (eds. du Sautoy, M., Segal, D. and Shalev, A.) (Birkhäuser, Boston, 2000), 121–179.CrossRefGoogle Scholar
Grigorchuk, R. I. and Wilson, J. S., ‘The uniqueness of the actions of certain branch groups on rooted trees’, Geom. Dedicata 100 (2003), 103–116.Google Scholar
Hardy, P. D., ‘Aspects of abstract and profinite group theory’, PhD Thesis, University of Birmingham, 2002.Google Scholar
Wilson, J. S., ‘Structure theory for branch groups’, in: Geometric and Homological Topics in Group Theory, London Mathematical Society Lecture Note Series, 358 (Cambridge University Press, Cambridge, 2009), 306–320.CrossRefGoogle Scholar