We prove that for all ergodic extensions S1 of a transformation by a locally compact second countable group G, and for all G-extensions S2 of an aperiodic transformation, there is a relative speedup of S1 that is relatively isomorphic to S2. We apply this result to give necessary and sufficient conditions for two ergodic n-point or countable extensions to be related in this way.

We give bounds on Kazhdan constants of abelian extensions of (finite) groups. As a corollary, we improved known results of Kazhdan constants for some meta-abelian groups and for the relatively free group in the variety of p-groups of lower p-series of class 2. Furthermore, we calculate Kazhdan constants of the tame automorphism groups of the free nilpotent groups.

We give an explicit description of the category central extensions a group scheme by sheaf Abelian groups. Based on this, we describe framework for computing with finite locally free commutative schemes, torsors under such schemes and groups isomorphism classes these objects.

We construct étale generalized Heisenberg group covers of hyperelliptic curves over number fields. use these to produce infinite families quadratic extensions cyclotomic fields that admit everywhere unramified Galois extensions.

In this paper we give some general results on the non-splitextension group $overline{G}_{n} = 2^{2n}{^{cdot}}Sp(2n,2), ngeq2.$ We then focus on the group $overline{G}_{4} =2^{8}{^{cdot}}Sp(8,2).$ We construct $overline{G}_{4}$ as apermutation group acting on 512 points. The conjugacy classes aredetermined using the coset analysis technique. Then we determine theinertia factor groups and Fischer...