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It is well known that Gassmann-Sunada group triples can be used to construct isospectral manifolds, arithmetically equivalent number fields, etc. (Recall that a Gassmann-Sunada triple $(U,V,W)$ consists of a group $U$ and subgroups $V, W$ such that every $U$-conjugacy class hits $V$ and $W$ in the same number of elements.) Starting from known triples, one can construct new ones using "trivial constructions," such as enlarging $U$, direct products, etc. My question now is: are there constructions known using tensor products of groups ? If so, are they "trivial" ?

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