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- W2318793306 abstract "Given a finite group G , the Frattini subgroup of G , Φ( G ) is defined to be the intersection of all the maximal subgroups of G . Of late there have been several attempts to consider generalizations of Φ( G ). For example, Gaschutz [ 7 ] and Rose [ 13 ] have investigated the intersection of all non-normal, maximal subgroups of a finite group. Deskins [ 6 ] has discussed the intersection of the family of maximal subgroups of a finite group whose indices are co-prime to a given prime. In [ 4-5, 12 ] we have considered the investigation of the family of all maximal subgroups of a finite group whose indices are composite and co-prime to a given prime. We have obtained several results about the family . In this paper which is a sequel to [ 4 ] we prove some further results about this family indicating the interesting role it plays especially when G is solvable or p -solvable. First we recall the main definition from [ 4 ]." @default.
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- W2318793306 date "1988-04-01" @default.
- W2318793306 modified "2023-09-25" @default.
- W2318793306 title "On the Intersection of a Family of Maximal Subgroups Containing the Sylow Subgroups of a Finite Group" @default.
- W2318793306 doi "https://doi.org/10.4153/cjm-1988-014-3" @default.
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