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Pointlike sets for varieties determined by groups
For a variety of finite groups , let denote
the variety of finite semigroups all of whose subgroups lie in . We
give a characterization of the subsets of a finite semigroup that are pointlike
with respect to . Our characterization is effective
whenever has a decidable membership problem. In particular, the
separation problem for -languages is decidable for any
decidable variety of finite groups . This generalizes Henckell's
theorem on decidability of aperiodic pointlikes