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Confined subgroups of Thompson's group F and its embeddings into wobbling groups
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<span title="2018-10-04">2018</span>
<i >
arXiv
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<span class="release-stage" >pre-print</span>
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<span title="2018-09-13">2018</span>
<span class="release-stage" >pre-print</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1809.05146v1">arXiv:1809.05146v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/exbyuiba7ba5pmkv3ochjwax24">fatcat:exbyuiba7ba5pmkv3ochjwax24</a> </span>
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We obtain a characterisation of confined subgroups of Thompson's group F. As a result, we deduce that orbital graph of a point under action of F has uniformly subexponential growth if and only if this point is fixed by the commutator subgroup. This allows us to prove non-embeddability of F into wobbling groups of graphs with uniformly subexponential growth.
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