紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2013, 50(2), p. 339-346

EULER CHARACTERISTICS ON A CLASS OF FINITELY GENERATED NILPOTENT GROUPS

Hamrouni, Hatem

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2013-06

A finitely generated torsion free nilpotent group is called an F-group. To each F-group Γ there is associated a connected, simply connected nilpotent Lie group G_Γ. Let TUF be the class of all F-group Γ such that G_Γ is totally unimodular. A group in TUF is called TUF-group. In this paper, we are interested in finding non-zero Euler characteristic on the class TUF and therefore, on TUFF, the class of groups K having a subgroup Γ of finite index in TUF. An immediate consequence we obtain that any two isomorphic finite index subgroups of a TUFF-group have the same index. As applications, we give two results, the first is a generalization of Belegradek's result, in which we prove that every TUFF-group is co-hopfian. The second is a known result due to G.C. Smith, asserting that every TUFF-group is not compressible.

10.18910/25090

25090

EULER CHARACTERISTICS ON A CLASS OF FINITELY GENERATED NILPOTENT GROUPS

Hamrouni, Hatem

Osaka University and Osaka City University, Departments of Mathematics

英語

2013-06

Osaka Journal of Mathematics

50

2

339

346

https://hdl.handle.net/11094/25090

10.18910/25090

https://doi.org/10.18910/25090