Special IMM groups

TL;DR

This paper discusses the construction of special hyperbolic groups with particular subgroup properties, extending previous work by Italiano-Martelli-Migliorini and Llosa Isenrich-Martelli-Py.

Contribution

It demonstrates that the hyperbolic groups constructed can be chosen to be special in the sense of Haglund-Wise, linking subgroup properties with specialness.

Findings

Hyperbolic groups with non-hyperbolic subgroups of finite type

Hyperbolic groups with subgroups of type F_3 but not F_4

Construction of special hyperbolic groups

Abstract

Italiano-Martelli-Migliorini recently constructed hyperbolic groups which have non-hyperbolic subgroups of finite type. Using a closely related construction, Llosa Isenrich-Martelli-Py constructed hyperbolic groups with subgroups of type $F_3$ but not $F_4$. We observe that these hyperbolic groups can be chosen to be special in the sense of Haglund-Wise.