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Norm rigidity for arithmetic and profinite groups
[article]
2023
arXiv
pre-print
Let A be a commutative ring, and assume every non-trivial ideal of A has finite-index. We show that if SL_n(A) has bounded elementary generation then every conjugation-invariant norm on it is either discrete or precompact. If G is any group satisfying this dichotomy we say that G has the dichotomy property. We relate the dichotomy property, as well as some natural variants of it, to other rigidity results in the theory of arithmetic and profinite groups such as the celebrated normal subgroup
arXiv:2105.04125v3
fatcat:7dki62yoebbydbyl7in5b2valm