149 research outputs found
A limit approach to group homology
In this paper, we consider for any free presentation of a group
the coinvariance of the -th tensor power of
the relation module and show that the homology group
may be identified with the limit of the groups
, where the limit is taken over the category of
these presentations of . We also consider the free Lie ring generated by the
relation module , in order to relate the limit of the groups
to the -torsion subgroup of
On certain questions of the free group automorphisms theory
Certain subgroups of the groups of automorphisms of a free group
are considered. Comparing Alexander polynomials of two poly-free groups
and we prove that these groups are not isomorphic, despite the
fact that they have a lot of common properties. This answers the question of
Cohen-Pakianathan-Vershinin-Wu from \cite{CVW}. The questions of linearity of
subgroups of are considered. As an application of the properties of
poison groups in the sense of Formanek and Procesi, we show that the groups of
the type for certain groups and the subgroup of
-automorphisms are not linear for . This
generalizes the recent result of Pettet that are not linear for
.Comment: 11 page
- β¦