Weakly finitely presented infinite periodic groups

Details Weakly finitely presented infinite periodic groups Weakly finitely presented infinite periodic groups

2002-09-18

arxiv.org/abs/math/0209234v1

Contemporary Math. 296(2002), 139-154

Mathematics

Group Theory

16 pages

Scientific paper

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.

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