An exponential A-group is a group which comes equipped with an A-action (A is a commutative ring with unity), satisfying certain axioms. In this paper, we investigate some aspects of root extraction in the category of exponential A-groups. Of particular interest is the extraction of roots in nilpotent R-powered groups. Among other results, we prove that if R is a PID and G is a nilpotent R-powered group for which root extraction is always possible, then the torsion R-subgroup of G lies in the center. Furthermore, if the torsion R-subgroup is finitely R-generated, then G is torsion-free.
1
Kingsborough Community College, Brooklyn, USA
2
Borough of Manhattan Community College, New York, USA
Stephen Majewicz; Marcos Zyman. On the extraction of roots in exponential $A$-groups. Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 835-846. doi: 10.4171/ggd/109
@article{10_4171_ggd_109,
author = {Stephen Majewicz and Marcos Zyman},
title = {On the extraction of roots in exponential $A$-groups},
journal = {Groups, geometry, and dynamics},
pages = {835--846},
year = {2010},
volume = {4},
number = {4},
doi = {10.4171/ggd/109},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/109/}
}
TY - JOUR
AU - Stephen Majewicz
AU - Marcos Zyman
TI - On the extraction of roots in exponential $A$-groups
JO - Groups, geometry, and dynamics
PY - 2010
SP - 835
EP - 846
VL - 4
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/109/
DO - 10.4171/ggd/109
ID - 10_4171_ggd_109
ER -
%0 Journal Article
%A Stephen Majewicz
%A Marcos Zyman
%T On the extraction of roots in exponential $A$-groups
%J Groups, geometry, and dynamics
%D 2010
%P 835-846
%V 4
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/109/
%R 10.4171/ggd/109
%F 10_4171_ggd_109
