# Weakly finitely presented infinite periodic groups

Research paper by S. V. Ivanov

Indexed on: 18 Sep '02Published on: 18 Sep '02Published in: Mathematics - Group Theory

#### Abstract

A group $G$ given by a presentation $G = < \mathcal A \| \mathcal R >$ is called weakly finitely presented if every finitely generated subgroup of $G$, generated by (images of) some words in $\mathcal A^{\pm 1}$, is naturally isomorphic to the subgroup of a group $G_0 = < \mathcal A_0 \| \mathcal R_0>$, where $\mathcal A_0 \subseteq \mathcal A$, $\mathcal R_0 \subseteq \mathcal R$ are finite, generated by (images of) the same words. In the article, weakly finitely presented periodic groups which are not locally finite are constructed.