Amenable groups without finitely presented amenable covers

Benli, MUSTAFA; Grigorchuk, Rostislav; de la Harpe, Pierre

doi:10.1007/s13373-013-0031-5

Amenable groups without finitely presented amenable covers

Benli M. G., Grigorchuk R., de la Harpe P.

BULLETIN OF MATHEMATICAL SCIENCES, cilt.3, sa.1, ss.73-131, 2013 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 3 Sayı: 1
Basım Tarihi: 2013
Doi Numarası: 10.1007/s13373-013-0031-5
Dergi Adı: BULLETIN OF MATHEMATICAL SCIENCES
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.73-131
Anahtar Kelimeler: Finitely generated groups, Finitely presented covers, Self-similar groups, Metabelian groups, Soluble groups, Groups of intermediate growth, Amenable groups, Groups with non-abelian free subgroups, Large groups, SOLUBLE GROUPS, GROWTH, AMENABILITY, TORSION, PRESENTATIONS, VALUATIONS, SUBGROUPS
Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups G with the following properties: (i) G is finitely generated, (ii) G is amenable, e.g. of intermediate growth, (iii) any finitely presented group with a quotient isomorphic to G contains non-abelian free subgroups, or the stronger (iii') any finitely presented group with a quotient isomorphic to G is large.