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Irrational-slope versions of thompson's groups T and V
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 1 / February 2022
- Published online by Cambridge University Press:
- 11 February 2022, pp. 244-262
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- Article
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In this paper, we consider the $T$
- and $V$
-versions, ${T_\tau }$
and ${V_\tau }$
, of the irrational slope Thompson group ${F_\tau }$
considered in J. Burillo, B. Nucinkis and L. Reeves [An irrational-slope Thompson's group, Publ. Mat. 65 (2021), 809–839]. We give infinite presentations for these groups and show how they can be represented by tree-pair diagrams similar to those for $T$
and $V$
. We also show that ${T_\tau }$
and ${V_\tau }$
have index-$2$
normal subgroups, unlike their original Thompson counterparts $T$
and $V$
. These index-$2$
subgroups are shown to be simple.
