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首页> 外文期刊>Journal of algebra and its applications >Characterizations of finite groups with σ-semiembedded subgroups
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Characterizations of finite groups with σ-semiembedded subgroups

机译：Characterizations of finite groups with σ-semiembedded subgroups

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Let σ={σi|i∈I} be a partition of the set of all primes ℙ, G a finite group and σ(G)={σi|σi∩π(|G|)≠∅}. A set ℋ of subgroups of G is said to be a complete Hallσ-set of G if every non-identity member of ℋ is a Hall σi-subgroup of G for some i∈I and ℋ contains exactly one Hall σi-subgroup of G for every σi∈σ(G). A subgroup H of G is said to be: σ-permutable in G if G has a complete Hall σ-set ℋ such that HAg=AgH for all A∈ℋ and all g∈G; σ-semipermutable in G if G has a complete Hall σ-set ℋ such that HAg=AgH for all g∈G and all σi-group A∈ℋ with σi∈σ(G)∖σ(H). We say that H is σ-semiembedded in G if there exists a σ-permutable subgroup T of G such that HT is a σ-permutable subgroup of G and H∩T≤HσsG, where HσsG denotes the subgroup of H which is generated by all σ-semipermutable subgroups of G contained in H. In this paper, we study the influence of σ-semiembedded subgroups on the structure of finite groups. Some known results are generalized and unified.

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