Self-similar groups of type FP_{n}
Dessislava H. Kochloukova, Said N. Sidki

TL;DR
This paper introduces new classes of self-similar groups, including S-arithmetic, affine, and metabelian groups, many of which are finitely presented and of type FP_{n}, expanding the understanding of their algebraic properties.
Contribution
It constructs novel self-similar groups such as S-arithmetic, affine, and metabelian groups, and analyzes their finiteness properties, especially their type FP_{n}.
Findings
Most soluble groups are finitely presented.
Many groups are of type FP_{n} for suitable n.
New classes of self-similar groups are introduced.
Abstract
We construct new classes of self-similar groups : S-aritmetic groups, affine groups and metabelian groups. Most of the soluble ones are finitely presented and of type FP_{n} for appropriate n.
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