On Two Questions of Itô
On Two Questions of Itô
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DOI：
10.1112/jlms/s1-29.1.84
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发表时间：
1954
影响因子：
1.2
通讯作者：
G. Higman;B. Neumann
中科院分区：
文献类型：
--
作者：
G. Higman;B. Neumann
1. 如果 0 是有限群，那么众所周知，0 的弗拉蒂尼子群（其最大子群的交集）是幂零的；如果 0 是 Hirsoh 的 tf-groupsj 之一，则同样如此。这导致 Noboru ltd 询问该财产是否可能无法普遍持有。然而，在本文中，我们提供了一些反例。我们构造的群没有最大子群，因此是它们自己的弗拉蒂尼子群，但它们绝不是幂零的，尽管它们是元布尔的。
1. If 0 is a finite group, then it is well known that the Frattini subgroup of 0—the intersection of its maximal subgroups—is nilpotentf; and the same is true if 0 is one of Hirsoh's tf-groupsj. This led Noboru ltd to enquire § whether the property might not hold generally. In this note, however, we provide some counter-examples The groups that we construct have no maximal subgroups and are, therefore, their own Frattini subgroups, but they are in no sense nilpotent, though they are metabelian.