关于可解ST-群的一个注记(英文)

A Note on Solvable ST-groups

有限群G被称为是一个ST-群,若对于子群H≤K≤L使得H在KS-中半正规,K在L中s-半正规,则有H在L中s-半正规.证明了对于含有素数幂阶的abnormal子群的有限群而言,可解ST-群类同可解T-群类和可解PT-群类是同一群类.

A finite group G is a ST-group, if, for subgroups H≤K≤L with H s-seminormal in K and K s-seminormal in L, it is always the case that H is s-seminormal in L It is shown that for finite groups containing abnormal subgroups of prime power order, the class of solvable ST-groups coincides with the class of solvable PT-groups and also coincides with the class of solvable T-groups.