关键词: 有限群, σ-置换子群, τ_σ-拟正规子群, 弱τ-嵌入子群, 弱τ_σ-嵌入子群

Abstract: By introducing  the notion of weakly τ_σ-embedded subgroups, sufficient conditions of σ-solubility and supersolubility of finite groups were given respectively in terms of weakly τ_σ-embedded subgroups, which generalized some existing results of supersolubility.

Key words: finite group, σ-permutable subgroup, τ_σ-quasinormal subgroup, weakly τ-embedded subgroup, weakly τ_σ-embedded subgroup