Cohomology of Split Group Extensions and Characteristic Classes

The Galois Cohomology of Square-Classes of Units in Klein-Four Group Extensions of Characteristic Not Two: A Thesis Submitted to the Department of Mathematics for Honors

GALOIS MODULE STRUCTURE OF pTH-POWER CLASSES OF EXTENSIONS OF DEGREE p

For fields F of characteristic not p containing a primitive pth root of unity, we determine the Galois module structure of the group of pth-power classes of K for all cyclic extensions K/F of degree p. The foundation of the study of the maximal p-extensions of fields K containing a primitive pth root of unity is a group of the pth-power classes of the field: by Kummer theory this group describe...

On the non-split extension group $2^{6}{^{cdot}}Sp(6,2)$

In this paper we first construct the non-split extension $overline{G}= 2^{6} {^{cdot}}Sp(6,2)$ as a permutation group acting on 128 points. We then determine the conjugacy classes using the coset analysis technique, inertia factor groups and Fischer matrices, which are required for the computations of the character table of $overline{G}$ by means of Clifford-Fischer Theory. There are two inerti...

Abelian Extensions of Algebras in Congruence-modular Varieties

We define abelian extensions of algebras in congruence-modular varieties. The theory is sufficiently general that it includes, in a natural way, extensions of R-modules for a ring R. We also define a cohomology theory, which we call clone cohomology, such that the cohomology group in dimension one is the group of equivalence classes of extensions.

On the non-split extension $2^{2n}{^{cdot}}Sp(2n,2)$

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...