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A Robinson characterization of finite -groups
Let be some partition of the set of all
primes and let be a finite group. Then is said to be -full if has a Hall -subgroup for all . A subgroup of
is said to be -permutable in provided is -full and
permutes with all Hall -subgroups of (that is,
) for all . We obtain a characterization of finite groups in
which -permutability is a transitive relation in , that is, if
is a -permutable subgroup of and is a -permutable
subgroup of , then is a -permutable subgroup of .Comment: 15 pages. arXiv admin note: text overlap with arXiv:1704.0250