Weakly finitely presented infinite periodic groups

2002/09/18 by S. V. Ivanov
Mathematics · #math.GR #msc:20E07 #msc:20F05 #msc:20F06 #msc:20F50

paper · pdf

published as Contemporary Math. 296(2002), 139-154 · 16 pages

arxiv created 2002/09/18 · arxiv updated 2009/11/30

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^{± 1}, is naturally isomorphic to the subgroup of a group G₀ = < \mathcal A₀ ‖ \mathcal R₀>, where \mathcal A₀ ⊆ \mathcal A, \mathcal R₀ ⊆ \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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