Abstract All groups are finite with denoting the Frattini subgroup of a group G. If G is nilpotent with subgroups H and K where then and However, as demonstrated by the symmetric group there are non-nilpotent groups that also satisfy these two properties. In 1965 H. Bechtell introduced a class of groups that satisfy the property that for all subgroups H of a group G. About 30 years later Doerk introduced a class of solvable groups that satisfy the property when for a group G. These two classes are identical when restricted to solvable groups. In this short paper, we will extend the work done by Bechtell and Doerk by presenting some additional properties and structural results concern this class of solvable groups.

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关于 Bechtell 和 Doerk 介绍的一类广义幂零群的注记

摘要 所有群都是有限的，表示群 G 的 Frattini 子群。如果 G 对子群 H 和 K 是幂零的，其中 和 但是，正如对称群所证明的那样，存在也满足这两个性质的非幂零群。1965 年，H. Bechtell 引入了一类群，它满足群 G 的所有子群 H 的性质。大约 30 年后，Doerk 引入了一类满足群 G 时性质的可解群。这两个类是相同的当限于可解群时。在这篇简短的论文中，我们将扩展 Bechtell 和 Doerk 所做的工作，介绍有关此类可解群的一些附加性质和结构结果。