One of the basic questions in number theory is to determine semi-simple l-adic representations of the absolute Galois group of a number field F . In case of abelian representations, a satisfactory answer is known for compatible system of l-adic representations, and these types of abelian representations are obtained from algebraic Hecke characters. In this paper, we discuss the question for two...

We study existentially closed CSA-groups. We prove that existentially closed CSA-groups without involutions are simple and divisible, and that their maximal abelian subgroups are conjugate. We also prove that every countable CSA-group without involutions embeds into a finitely generated one having the same maximal abelian subgroups, except maybe the infinite cyclic ones. We deduce from this tha...

For every prime p and integer n > 3 we explicitly construct an abelian variety A/Fpn of dimension n such that for a suitable prime l the group of quasi-isogenies of A/Fpn of l-power degree is canonically a dense subgroup of the n-th Morava stabilizer group at p. We also give a variant of this result taking into account a polarization. This is motivated by the recent construction of topological ...

The structure of the automorphism group of a simple TAI algebra is studied. In particular, we show that Inn(A) Inn0(A) is isomorphic (as a topological group) to an inverse limit of discrete abelian groups for a unital, simple, AH algebra with bounded dimension growth. Consequently, Inn(A) Inn0(A) is totally disconnected. Another consequence of our results is the following: Suppose A is the tran...

we say that a finite group $g$ is conjugacy expansive if for anynormal subset $s$ and any conjugacy class $c$ of $g$ the normalset $sc$ consists of at least as many conjugacy classes of $g$ as$s$ does. halasi, mar'oti, sidki, bezerra have shown that a groupis conjugacy expansive if and only if it is a direct product ofconjugacy expansive simple or abelian groups.by considering a character analo...

Abstract For a mixing shift of finite type, the associated automorphism group has rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce stabilization group, study its properties, use them many stabilized groups. also show that for full shift, subgroup generated by elements order is simple an extension free abelian rank this group.

This paper continues the study of generalized amalgamation properties begun in [1], [2], [3], [5], and [6]. Part of the paper provides a finer analysis of the groupoids that arise from failure of 3-uniqueness in a stable theory. We show that such groupoids must be abelian and we link the binding group of the groupoids to a certain automorphism group of the monster model, showing that the group ...