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Let be some partition of the set of all primes , be a finite group and . A set of subgroups of is said to be a complete Hall -set of if every non-identity member of is a Hall -subgroup of and contains exactly one Hall -subgroup of for every . is said to be -full if possesses a complete Hall -set. A subgroup of is -permutable in if possesses a complete Hall -set such that = for all and all . A subgroup of is -permutably embedded in if is -full...
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