## On a notion of closeness of groups.(English)Zbl 1325.43004

The authors show that if two groups are close enough to each other and one of them has the property that the orders of its elements have a uniform finite upper bound, then these two groups are isomorphic.

### MSC:

 43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) 43A20 $$L^1$$-algebras on groups, semigroups, etc.

### Keywords:

discrete group; group representation; distance
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