Homogeneous Functions and Algebraic \(K\)--theory

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 \(x\). W...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Dennis, R Keith, Laubenbacher, Reinhard C
Format: Article
Language:English
Subjects:
Group theory
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Summary: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.
ISSN:2331-8422