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arXiv · 2306.11940

Homogeneous Functions and Algebraic $K$--theory

R. Keith Dennis·Reinhard C. Laubenbacher
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Abstract

In this paper we develop the theory of homogeneous functions between finite abelian groups. Here, a function $f:G\longrightarrow H$ between finite abelian groups is homogeneous of degree $d$ if $f(nx)=n^df(x)$ for all $x\in G$ 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 $\mathbb{Q}/\mathbb{Z}$ maps onto $SK_1(\mathbb{Z}[G])$, generalizing a result of R. Oliver for $p$-groups.

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R. Keith Dennis, Reinhard C. Laubenbacher. 2023-06-20. Homogeneous Functions and Algebraic $K$--theory. https://arxiv.org/abs/2306.11940

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