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Large scale properties of groups; growth functions; Dehn functions; small cancellation properties; hyperbolicity and CAT(0); actions and representations; combinatorial group theory; presentations

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every element with eigenvalue 1

Is there a "non-trivial" subgroup $G$ of $GL(n,\mathbb C)$ whose every element has an eigenvalue $1$? "Non-trivial" here means that is no common eigenvector with eigenvalue $1$ for all elements of $ …
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