$K_1$-groups via binary complexes of fixed length

Exterior Power Operations on Higher K-groups via Binary Complexes

We use Grayson’s binary multicomplex presentation of algebraic K-theory to give a new construction of exterior power operations on the higher K-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a λ-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial f...

Algebraic K-theory via binary complexes

In [11], Quillen defines the notion of exact category. Each such category N is an additive category together with a suitable collection of sequences called short exact sequences. Quillen constructs a space by gluing simplices to each other, using the exact sequences of N to determine the simplices and the gluing instructions. Then for each n ∈ N he defines KnN as a homotopy group of the space. ...

On the Length of Finite Groups and of Fixed Points

The generalized Fitting height of a finite group G is the least number h = h∗(G) such that F ∗ h (G) = G, where the F ∗ i (G) is the generalized Fitting series: F ∗ 1 (G) = F ∗(G) and F ∗ i+1(G) is the inverse image of F ∗(G/F ∗ i (G)). It is proved that if G admits a soluble group of automorphisms A of coprime order, then h∗(G) is bounded in terms of h∗(CG(A)), where CG(A) is the fixed-point s...

Ruthenium(II)-Pyridylamine Complexes Having Functional Groups via Amide Linkages

E ective Variable - Length - to - Fixed - Length Coding via a Re - Pair Algorithm

We address the problem of improving variable-length-toxed-length codes (VF codes). A VF code is an encoding scheme that uses a xed-length code, and thus, one can easily access the compressed data. However, conventional VF codes usually have an inferior compression ratio to that of variable-length codes. Although a method proposed by T. Uemura et al. in 2010 achieves a good compression ratio com...