Inverting Integers in Tambara Functors

Abstract

Let $G$ be a finite group. A $G$-Tambara functor $T$ consists of collection of commutative rings $T(G/H)$ (one for each subgroup $H$ of $G$), together with certain structure maps, satisfying certain axioms. In this note, we show that, for any integer $k$, any $G$-Tambara functor $T$, and any subgroups $H_1, H_2 \leq G$, $k$ is a unit in $T(G/H_1)$ if and only if $k$ is a unit in $T(G/H_2)$.

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