What is $\widehat{G}$ here in transfer kernel?

Question

I'm reading a paper by A. WEISS and K.W. GRUENBERG "Captilulation and transfer kernels"

(Can be found here.)

It says:

It used $\widehat{G}$ to denote norm map $m\mapsto \sum_g gm$ for some $G$-module $M$ before, but doens't seem to be the case here.

I find some conventions denoting $\widehat{G}$ as a character of the group, but this is a map $G\rightarrow \mathbb C^{\times}$ and seems only restricted to abelian groups.

So what is the definition of $\widehat{G}$ in $\Lambda$? It never states it in the paper.

Answer 1

I think it's just $\hat{G}=\sum_{g\in G}g$. So you would have $\Lambda = \mathbb{Z}G/\hat{G}\mathbb{Z}$.

There's a newer paper that's typeset a little better you may be interested in looking at.