Timeline for The definition of Higman-Thompson group
Current License: CC BY-SA 4.0
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| Mar 13, 2022 at 9:59 | comment | added | YCor | Additional remark: let $F_{n,m}$ be a free $n$-Jonsson-Tarski ($n$-JS) algebra on $m$ generators $x_1,\dots,x_m$. $n$-JS algebra $A$ means a set endowed with a bijective law $A^n\to A$. The inverse is an $n$-tuple of unary laws $u_i:A\to A$. From the $x_j$ draw $m$ labeled regular rooted trees by joining $x_j$ to $u_ix_j$, $u_jx_j$ to $u_{j'}u_jx_i$, and so on. Then the automorphism group of $F_{n,m}$ induces the given near action on this forest. In the other way round, one can thus view $F_{n,m}$ as an "enveloping action" to the near action of $G_{n,m}$ on $F_{n,m}$. | |
| Mar 10, 2022 at 12:24 | history | answered | YCor | CC BY-SA 4.0 |