In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and certain geometric and measure or orbit equivalence invariants of groups on the other. This leads to many new examples of groups not presentable by products, including all groups with infinitely many ends, the (outer) automorphism groups of free groups, Thompson’s groups, and even some elementary amenable groups.
@article{10_4171_ggd_180,
author = {D. Kotschick and Clara L\"oh},
title = {Groups not presentable by products},
journal = {Groups, geometry, and dynamics},
pages = {181--204},
year = {2013},
volume = {7},
number = {1},
doi = {10.4171/ggd/180},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/180/}
}
TY - JOUR
AU - D. Kotschick
AU - Clara Löh
TI - Groups not presentable by products
JO - Groups, geometry, and dynamics
PY - 2013
SP - 181
EP - 204
VL - 7
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/180/
DO - 10.4171/ggd/180
ID - 10_4171_ggd_180
ER -
%0 Journal Article
%A D. Kotschick
%A Clara Löh
%T Groups not presentable by products
%J Groups, geometry, and dynamics
%D 2013
%P 181-204
%V 7
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/180/
%R 10.4171/ggd/180
%F 10_4171_ggd_180
