The class group of an absolutely Abelian $l$-extension

Every Abelian Group Is a Class Group

Let T be the set of minimal primes of a Krull domain A. If S is a subset of T9 we form B = n AP for PeS and study the relation of the class group of B to that of A. We find that the class group of B is always a homomorphic image of that of A. We use this type of construction to obtain a Krull domain with specified class group and then alter such a Krull domain to obtain a Dedekind domain with t...

Abelian covers of surfaces and the homology of the level L mapping class group

We calculate the first homology group of the mapping class group with coefficients in the first rational homology group of the universal abelian Z/LZ-cover of the surface. If the surface has one marked point, then the answer is Qτ(L), where τ(L) is the number of positive divisors of L. If the surface instead has one boundary component, then the answer is Q. We also perform the same calculation ...

Abelian and Solvable Subgroups of the Mapping Class Group Joan

Finite abelian subgroups of the mapping class group

Let S be a closed, smooth, orientable surface of genus 2. The mapping class group M of S (or MCG) is the group of isotopy classes of homeomorphisms of S . In this paper we shall investigate the conjugacy classes of finite elementary abelian subgroups, and more generally the finite abelian subgroups of M . While the general finite subgroup classification is important we focus on the case where G...

Solvable $L$-subgroup of an $L$-group

In this paper, we study the notion of solvable $L$-subgroup of an $L$-group and provide its level subset characterization and this justifies the suitability of this extension. Throughout this work, we have used normality of an $L$-subgroup of an $L$-group in the sense of Wu rather than Liu.