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- W2384348889 abstract "In this paper, the theorems of Doerk, Asaad and Kegel for supersolvable groups are generalized to:Theorem 1 If the indices of subgroups Ai, i=1,2,3,4 in a group G are relatively prime in pairs and Ai, i=1,2,3 are supersolvable, A4 is metanilpotent, then G is supersolvable.Theorem 2 Suppose that the indices of subgroups A, B, C in a group G are relatively prime in pairs and square free. If A, B are supersolvable and C is metanilpotent, then G is supersolvable.Let n(G) = {p1, ... , pn}. Group G is called general nilpotent if there exists a system of Sylow subgroups Pi, ∈Sylp, G, i=1,2…,n, such that aiaj = ajai for any ai∈Pi, aj∈Pj.Theorem 3 Let the order of a group G be odd and G=AB=BC=CA. If A, B are general nilpotent and C is supersolvable, then G is supersolvable.The theorem of PycaKo is generalized toTheorem 4 Let H be a general nilpotent II-Hall subgroup of a group G,= {P1…Pk-1pk}. If the sylow pi-subgroup of G, i=1,2,…, k-1 is metacyclic and the sylow 2-subgroup is cyclic, or 3 |H| when p1 = 2) then any -subgroup K is contained in H conjugately. In particular, any two -Hall subgroups of G are conjugate." @default.
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- W2384348889 date "1986-01-01" @default.
- W2384348889 modified "2023-09-25" @default.
- W2384348889 title "SEVERAL THEOREMS ON SUPERSOLVABLE FINITE GROUPS" @default.
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