Abstract.
In this paper, we study partial group actions on 2-complexes. Our results include a characterization, in terms of generating sets, of when a partial group action on a connected 2-complex has a connected globalization. Using this result, we give a short combinatorial proof that a group acting without fixed points on a connected 2-complex, with finite quotient, is finitely generated. This result is then generalized to characterize finitely generated groups as precisely those groups having a partial action, without fixed points, on a finite tree, with a connected globalization. Finally, using Bass-Serre theory, we determine when a partial group action on a graph has a globalization which is a tree.
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The author was supported in part by NSF-NATO postdoctoral fellowship DGE-9972697, by Praxis XXI scholarship BPD 16306 98 and by FCT through Centro de Matemática da Universidade do Porto.
Received September 20, 2001; in revised form June 25, 2002
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Steinberg, B. Partial Actions of Groups on Cell Complexes. Monatsh. Math. 138, 159–170 (2003). https://doi.org/10.1007/s00605-002-0521-0
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DOI: https://doi.org/10.1007/s00605-002-0521-0