论文标题
在有限组的某些产品上
On some products of finite groups
论文作者
论文摘要
Baer的经典结果指出，有限的组$ G $是两个正常的超溶子组的产物，并且仅当$ g'$是nilpotent时，才是超溶的。在本文中，我们表明，如果$ g = ab $是supersoluble（分别分别为$ w $ - supersoluble）子组的子群体$ a $ a $ a $ a $ and $ b $，$ a $在$ g $，$ g $，$ b $中，每个最大亚组的每个sylow sylow subgroup a $ a $ a $ a $ a $ a $ a $ a $ $ suplu glu's suplu quble（分别是$ wuble） nilpotent。当$ a \ cap b = 1 $并获得更多一般结果时，我们还研究了上面定义的子组的产品。
A classical result of Baer states that a finite group $ G $ which is the product of two normal supersoluble subgroups is supersoluble if and only if $ G' $ is nilpotent. In this article we show that if $ G=AB $ is the product of supersoluble (respectively, $ w $-supersoluble) subgroups $ A $ and $ B $, $ A $ is normal in $ G $, $ B $ permutes with every maximal subgroup of each Sylow subgroup of $ A $, then $ G $ is supersoluble (respectively, $ w $-supersoluble) provided that $ G' $ is nilpotent. We also investigate products of subgroups defined above when $ A\cap B=1 $ and obtain more general results.
