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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.15206 |
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| _version_ | 1866910147299770368 |
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| author | Amir, Gideon Angel, Omer Virag, Balint |
| author_facet | Amir, Gideon Angel, Omer Virag, Balint |
| contents | We give lower bounds for the electrical resistance between vertices in the Schreier graphs of the action of the linear (degree 1) and quadratic (degree 2) mother groups on the orbit of the zero ray. These bounds, combined with results of \cite{JNS} show that every quadratic activity automaton group is amenable. The resistance bounds use an apparently new "weighted" version of the Nash-Williams criterion which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_15206 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Amenability of quadratic automaton groups Amir, Gideon Angel, Omer Virag, Balint Group Theory Probability 60B15, 43A07, 20E08 We give lower bounds for the electrical resistance between vertices in the Schreier graphs of the action of the linear (degree 1) and quadratic (degree 2) mother groups on the orbit of the zero ray. These bounds, combined with results of \cite{JNS} show that every quadratic activity automaton group is amenable. The resistance bounds use an apparently new "weighted" version of the Nash-Williams criterion which may be of independent interest. |
| title | Amenability of quadratic automaton groups |
| topic | Group Theory Probability 60B15, 43A07, 20E08 |
| url | https://arxiv.org/abs/2111.15206 |