Decomposition and Inertia Groups in $\mathbf{Z}_p$-Extensions

Inertia Groups and Fibers

Let X and Y be proper, normal, connected schemes over a field K, and let f : X → Y be a finite, flat K-morphism which is generically Galois (i.e., the extension of function fields K(Y ) ↪→ K(X) is Galois) with Galois group G. It is well-known that for the Zariski-open complement U ⊆ Y of the branch locus of f , the map f−1(U) → U is a (right) G-torsor. Thus, for any y ∈ U and x ∈ f−1(y), the ex...

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

A decomposition of the manipulator inertia matrix

Algebraic extensions in free groups

The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were given. We develop a theory of algebraic extensions for free groups, highlighting the analogies and differences with respect to the corresponding classical field-...

Extensions of Groups

To better understand groups it is often useful to see how a group can be built from smaller groups. For example, given two groups G and H, we can form the direct product G × H. This new group can be studied in terms of the two pieces from which it is built. However, the direct product construction is too special to understand most groups. In other words, most groups are not expressible as the d...