ON INNERπ'-CLOSED GROUPS AND NORMAL π-COMPLEMENTS |
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引用本文: | 王晓峰.ON INNERπ'-CLOSED GROUPS AND NORMAL π-COMPLEMENTS[J].数学年刊B辑(英文版),1989(3). |
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作者姓名: | 王晓峰 |
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作者单位: | Depatrtment of |
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摘 要: | In this paper, the author classifies the finite inner π′-closed groups, and proves the following results1. If each proper subgroup K of a group G is weak π-homogeneous and weak π′-homogeneous, then G is a Schmidt group, or a direct product of two Hall subgroups.2. If G is a weak π-homogeneous group, then G is π′-closed if one of the following statements is true: (1)Each π-subgroup of G is 2-closed. (2) Each π-subgroup of G is 2′-closed.3. Let G be a group and π be a set of odd primes. If N_G(Z(J(P))) has a normal π-completement for a Sytow p-subgroup of G with prime ρ in π then so does G.
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