论文标题
$π$ - 元素和nilpotent/abelian Hall $π$ -subgroups的连词类别
Conjugacy classes of $π$-elements and nilpotent/abelian Hall $π$-subgroups
论文作者
论文摘要
令$ g $为有限的组，$π$是一组素数。我们研究有大量$π$元素的有限群体。特别是，我们根据$ g $的$π$ - 部分获得了此数字的精确下限，以确保在$ g $中存在Nilpotent或Abelian Hall $π$ -subgroup。
Let $G$ be a finite group and $π$ be a set of primes. We study finite groups with a large number of conjugacy classes of $π$-elements. In particular, we obtain precise lower bounds for this number in terms of the $π$-part of the order of $G$ to ensure the existence of a nilpotent or abelian Hall $π$-subgroup in $G$.
