On a class of finite solvable groups
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AbstractA finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms.
2019 ◽
Vol 18
(04)
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pp. 1950074
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1991 ◽
Vol 34
(3)
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pp. 423-425
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2019 ◽
Vol 19
(10)
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pp. 2050190
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1975 ◽
Vol 20
(1)
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pp. 25-32
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2021 ◽
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2010 ◽
Vol 17
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pp. 925-927
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2001 ◽
Vol 38
(1-4)
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pp. 339-355
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2016 ◽
Vol 104
(1)
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pp. 37-43
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