1. The main theorems revisited We now state in more detail the main theorems of class field theory. However, we need two more preliminary definitions: Definition 1.1. Given an extension L/K of number fields, and a fractional ideal I of L, we define the fractional ideal N L/K (I) of K as follows: write I = i q ei i , let p i = q i ∩ O K , and let N L/K (I) = i p eifi i. Definition 1.2. Let σ : K...

We prove a variant of the well-known Reidemeister-Schreier Theorem for finitely L-presented groups. More precisely, we prove that each finite index subgroup of a finitely L-presented group is itself finitely L-presented. Our proof is constructive and it yields a finite L-presentation for the subgroup. We further study conditions on a finite index subgroup of an invariantly finitely L-presented ...

We prove that the quotient of integer homology cobordism group by subgroup generated Seifert fibered spaces is infinitely generated.

1. DEFINITIONS. Let D be the unit disk {z\ \z\ < l } and let £ be the group of conformai homeomorphisms of D. A Fuchsian group is a discrete subgroup of <£. We shall be concerned here with the finitely generated Fuchsian groups. It is known that these have the following presentations. Generators: aïy bi, • • • , ag, bg, eh • • • , ek, fa, • • • , hm, pu • * * , pr. Defining relations : e? = eg ...

We give a geometric interpretation of Milnor's invariants ¯ µ(ijk) in terms of triple intersection points of Seifert surfaces for the three link components. This generalizes ideas from Cochran [Co] to links which are not algebraically split. We recall how to compute ¯ µ(ijk) from Milnor [Mi]. Given a link L, its link group π 1 (S 3 − L) has a Wirtinger presentation, generated by the arcs of the...

TO subgroup strains of Theiler's murine encephalomyelitis virus (TMEV) synthesize L* protein from an alternative initiation codon. We first demonstrated L* expression in the central nervous system (CNS) of TMEV-infected mice during the acute phase of infection by immunoprecipitation and immunoblotting with anti-L* antibody. In addition, we generated mutant viruses which synthesize FLAG or 3xFLA...

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

Let G be a connected, simply-connected, almost simple algebraic group of simplylaced type over C and let σ be a diagram automorphism of G. Let Gσ = ((G)) be the L-dual of the fixed point subgroup of σ on the L-dual of G. In this paper we relate the character of a finite dimensional irreducible representation of the disconnected algebraic group G〈σ〉 (generated by G and σ) on the connected compon...

Let L be the function field of a projective space P n k over an algebraically closed field k of characteristic zero, and H be the group of projective transformations. An H-sheaf V on P n k is a collection of isomorphisms V −→ g * V for each g ∈ H satisfying the chain rule. We construct, for any n > 1, a fully faithful functor from the category of finite-dimensional L-semi-linear representations...

Let L be the function field of a projective space P n k over an algebraically closed field k of characteristic zero, and H be the group of projective transformations. An H-sheaf V on P n k is a collection of isomorphisms V −→ g * V for each g ∈ H satisfying the chain rule. We construct, for any n > 1, a fully faithful functor from the category of finite-dimensional L-semi-linear representations...