On X-Permutable Subgroups
A subgroup A of a group G is said to be X-permutable with another subgroup B in G, where ∅ ≠ X ⊆ G, if there exists some element x ∈ X such that ABx=BxA. In this paper, the solubility and supersolubility of finite groups are described by X-permutability of the Hall subgroups and their subgroups, in addition, the well known theorem of Schur-Zassenhaus in finite group is generalized.
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2011 ◽
Vol 10
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pp. 811-820
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2009 ◽
Vol 52
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pp. 145-150
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2014 ◽
Vol 56
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pp. 691-703
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1969 ◽
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2017 ◽
Vol 16
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pp. 1750224
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