Abstract
Let ℱ be a subgroup-closed saturated formation. A finite group G is called an ℱpc-group provided that each subgroup X of G is ℱ-subabnormal in the ℱ-subnormal closure of X in G. Let ℱpc be the class of all ℱpc-groups. We study some properties of ℱ pc-groups and describe the structure of ℱpc-groups when ℱ is the class of all soluble π-closed groups, where π is a given nonempty set of prime numbers.
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