Letσ={σ_(i)|i∈I}be some partition of all primes P and G a finite group.A subgroup H of G is said to beσ-subnormal in G if there exists a subgroup chain H=H_(0)≤H_(1)≤・・・≤Hn=G such that either H_(i−1)is normal i...Letσ={σ_(i)|i∈I}be some partition of all primes P and G a finite group.A subgroup H of G is said to beσ-subnormal in G if there exists a subgroup chain H=H_(0)≤H_(1)≤・・・≤Hn=G such that either H_(i−1)is normal in Hi or Hi/(H_(i−1))Hi is a finiteσj-group for some j∈I for i=1,...,n.We call a finite group G a T_(σ)-group if everyσ-subnormal subgroup is normal in G.In this paper,we analyse the structure of the T_(σ)-groups and give some characterisations of the T_(σ)-groups.展开更多
文摘Letσ={σ_(i)|i∈I}be some partition of all primes P and G a finite group.A subgroup H of G is said to beσ-subnormal in G if there exists a subgroup chain H=H_(0)≤H_(1)≤・・・≤Hn=G such that either H_(i−1)is normal in Hi or Hi/(H_(i−1))Hi is a finiteσj-group for some j∈I for i=1,...,n.We call a finite group G a T_(σ)-group if everyσ-subnormal subgroup is normal in G.In this paper,we analyse the structure of the T_(σ)-groups and give some characterisations of the T_(σ)-groups.
