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A set ${\\cal H}$ of subgroups of a finite group $G$ is said to be a \\emph{ complete Hall $\\Pi $-set} of $G$ if every member of ${\\cal H}$ is a Hall $\\sigma_{i}$-subgroup of $G$ for some $\\sigma_{i}\\in \\Pi$ and ${\\cal H}$ contains exact one Hall $\\sigma_{i}$-subgroup of $G$ for every $\\sigma_{i}\\in \\Pi$ such that $\\sigma_i\\cap \\pi(G)\\neq\\emptyset$. 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A set ${\\cal H}$ of subgroups of a finite group $G$ is said to be a \\emph{ complete Hall $\\Pi $-set} of $G$ if every member of ${\\cal H}$ is a Hall $\\sigma_{i}$-subgroup of $G$ for some $\\sigma_{i}\\in \\Pi$ and ${\\cal H}$ contains exact one Hall $\\sigma_{i}$-subgroup of $G$ for every $\\sigma_{i}\\in \\Pi$ such that $\\sigma_i\\cap \\pi(G)\\neq\\emptyset$. 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