Overview
The Department is saddened by the death of our colleague and friend Keith. Read more here.
Publications
- Recent developments in digital library technologies (with G. O. Michler, M. Suzuki and G. Schneider); in DIAR-03: Workshop on Document Image Analysis and Retrieval, to appear.
- Computation of the Scharlau invariant (with Paul Young), in preparation.
- The number of groups of order n, in preparation.
- Generic product decompositions of finite groups, in preparation.
- K. Dennis, G. O. Michler, G. Schneider and M. Suzuki, "Automatic
reference linking in distributed digital libraries," 2003 Conference
on Computer Vision and Pattern Recognition Workshop, Madison, WI, USA,
2003, pp. 26-26, doi: 10.1109/CVPRW.2003.10026. https://ieeexplore.ieee.org/document/4624284?arnumber=4624284. - arXiv:2306.11940 (https://arxiv.org/pdf/2306.11940.pdf)
Mathematics > K-Theory and Homology
[Submitted on 20 Jun 2023]
Homogeneous Functions and Algebraic K--theory
R. Keith Dennis, Reinhard C. Laubenbacher
In this paper we develop the theory of homogeneous functions between finite abelian groups. Here, a function f:G⟶H between finite abelian groups is homogeneous of degree d if f(nx)=ndf(x) for all x∈G and all n which are relatively prime to the order of x. We show that the group of homogeneous functions of degree one from a group G of odd order to ℚ/ℤ maps onto SK1(ℤ[G]), generalizing a result of R. Oliver for p-groups.