# R. Keith Dennis

## Professor Emeritus

### 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:GâŸ¶H between finite abelian groups is homogeneous of degree d if f(nx)=ndf(x) for all xâˆˆG 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 â„š/â„¤ maps onto SK1(â„¤[G]), generalizing a result of R. Oliver for p-groups.

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