论文标题
在某些适合拟合的应用中，例如有限组的子组
On some applications of Fitting like subgroups of finite groups
论文作者
论文摘要
在本文中，我们研究了所有最大或所有Sylow子组的组为$ K $ - $ \ MATHFRAK {F} $ - 在其产品中的亚正常，并具有拟合子组$ \ Mathrm {f}^*（g）$和$ \ Mathrm {\ Mathrm {\ tilde f}（g）（g）（g）（g）$。我们证明，遗传形式$ \ mathfrak {f} $包含每个组的Sylow子组为$ K $ - $ \ $ \ MATHFRAK {f} $ - 在其产品中使用$ \ MATHRM {f}^*（g）$ for $ \ m athfrak $ clast $ clast $ n $ clast-所有素数的集合。我们获得了$σ$ -NILPOTENT超中心的新特征，即$ \ Mathfrak {f} $ - 超级中心和正常的最大子组，$ k $ - $ \ $ \ mathfrak {f} $ - subnormalalyal subnormalaly subnormalial sylow sylow sub groups yf $ \ mathfrak $ cost $ nist $ ins $ is last $ rpsent us $ rpsent us $ rps last $ rp y}
In this paper we study the groups all whose maximal or all Sylow subgroups are $K$-$\mathfrak{F}$-subnormal in their product the with generalizations of the Fitting subgroup $\mathrm{F}^*(G)$ and $\mathrm{\tilde F}(G)$. We prove that a hereditary formation $\mathfrak{F}$ contains every group all whose Sylow subgroups are $K$-$\mathfrak{F}$-subnormal in their product with $\mathrm{F}^*(G)$ if and only if $\mathfrak{F}$ is the class of all $σ$-nilpotent groups for some partition $σ$ of the set of all primes. We obtain a new characterization of the $σ$-nilpotent hypercenter, i.e. the $\mathfrak{F}$-hypercenter and the normal largest subgroup which $K$-$\mathfrak{F}$-subnormalize all Sylow subgroups coincide if and only if $\mathfrak{F}$ is the class of all $σ$-nilpotent groups.
