For mixed-identity-free groups G, the projective unitary group of L(G) contains a maximal discrete subgroup containing G.
Helling, Bestimmung der Kommensurabilit¨ atsklasse der Hilbertsch en Modulgruppe , Math
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Maximal discrete subgroups in unitary groups of operator algebras
For mixed-identity-free groups G, the projective unitary group of L(G) contains a maximal discrete subgroup containing G.