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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus


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Online
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1435-4446
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Volume 15, Issue 6

Issues

Normal subgroups of groups acting on trees and automorphism groups of graphs

Rögnvaldur G. Möller / Jan Vonk
Published Online: 2012-11-01 | DOI: https://doi.org/10.1515/jgt-2012-0029

Abstract.

Let T be a tree and e an edge in T. If C is a component of and both C and its complement are infinite, we say that C is a half-tree. The main result of this paper is that if G is a closed subgroup of the automorphism group of T and G leaves no non-trivial subtree invariant and fixes no end of T, then the subgroup generated by the pointwise stabilizers of half-trees is topologically simple. This result is used to derive analogues of recent results of Caprace and De Medts (2011) and it is also applied in the study of the full automorphism group of a locally finite primitive graph with infinitely many ends.

About the article

Received: 2012-06-20

Revised: 2012-08-07

Published Online: 2012-11-01

Published in Print: 2012-11-01


Citation Information: Journal of Group Theory, Volume 15, Issue 6, Pages 831–850, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt-2012-0029.

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[1]
PIERRE-EMMANUEL CAPRACE, COLIN D. REID, and GEORGE A. WILLIS
Forum of Mathematics, Sigma, 2017, Volume 5
[2]
PIERRE-EMMANUEL CAPRACE, COLIN D. REID, and GEORGE A. WILLIS
Forum of Mathematics, Sigma, 2017, Volume 5

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