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A subgroup A of a finite group G is called Φ-isolator of G if A covers the Frattini chief factors of G and avoids the supplemented ones. Let H be a Φ-isolator of a soluble finite group G. In the present paper, we prove that there exist elements x , y ∈ G such that the equality H ∩ H x ∩ H y = Φ (G) holds. This result is an answer to Question 19.38 in "The Kourovka notebook". [ABSTRACT FROM AUTHOR]