Finite groups with abnormal or formational subnormal primary subgroups

被引:5
|
作者
Monakhov, Victor S. [1 ]
Sokhor, Irina L. [2 ]
机构
[1] Gomel F Scorina State Univ, Dept Math, Gomel, BELARUS
[2] Brest State AS Pushkin Univ, Dept Phys & Math, Brest, BELARUS
关键词
Abnormal subgroup; finite groups; primary subgroup; subnormal subgroup;
D O I
10.1080/00927872.2019.1572174
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A subgroup H of a group G is abnormal if for every . A group is primary if its order is equal to a power of a prime. We indicate the structure of a finite group in which primary cyclic subgroups are abnormal or subnormal. We investigate finite groups with abnormal or formational subnormal primary subgroups for a subgroup-closed saturate lattice formation that contained all nilpotent subgroups. We also describe the structure of a group G in which every subgroup is abnormal or -subnormal. In particular, G has a generalized Sylow tower and every non-abnormal subgroup of G is supersoluble.
引用
收藏
页码:3941 / 3949
页数:9
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