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- W2036158585 abstract "A p-soluble group G belongs to the class F(n, p) whenever the ranks of the p-chief factors of G divide n and G has order coprime to n. A group in F(n, p) is characterised by the embedding of its maximal subgroups. Whenever N1 and N2 are normal subgroups of G, of coprime indices in G, which lie in F(n, p), then G lies in F(n, p) also. F(n) denotes the intersection, taken over all primes p, of the classes F(n, p). Simple groups all of whose proper subgroups lie in F(n) are determined. Given an integer n > 2, there exist an integer m with the same prime divisors as n and a soluble group G such that G lies in F(m) but G does not possess a Sylow tower. (We may take m = n provided that n is not a multiple of 1806.) Furthermore, when n is odd, an example of a soluble group G, all of whose proper subgroups lie in F(n) but G has no Sylow tower, is given." @default.
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- W2036158585 date "1975-01-01" @default.
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- W2036158585 title "A generalisation of supersoluble groups" @default.
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- W2036158585 doi "https://doi.org/10.1090/s0002-9947-1975-0372023-2" @default.
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