Abstract
UDC 512.542 Let be some partition of the set of all primes and let be a nonempty subset of the set A set of subgroups of a finite group is said to be a \emph{complete Hall -set} of if every member of is a Hall -subgroup of for some and contains exactly one Hall -subgroup of for every such that A subgroup of is called (i) {-<em>permutable</em>} if for and ; (ii) {-<em>permutable</em> in } if is -permutable for some complete Hall -set of We study the influence of -permutable subgroups on the structure of In particular, we prove that if and where and are -permutable -separable (respectively, -closed) subgroups of then is also -separable (respectively, -closed). Some known results are generalized.
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