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We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.
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