Determining the Frattini Subgroup from the Character Table
Determining the Frattini Subgroup from the Character Table
复制标题
从字符表确定 Frattini 子群
DOI：
10.4153/cjm-1976-055-0
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
S. Garrison
中科院分区：
文献类型：
--
作者：
S. Garrison
Brauer [1，p. 141]讨论了一个群的哪些子群可以从它的特征标表中确定的问题。他提到，指的是p-团体，弗拉蒂尼小组可以确定。证明了对于任意有限可解群，Frattini子群可以由特征标表确定。然后我们展示无限多个不可解群对，使得给定对的两个成员具有相同的特征标表，但具有不同阶的弗拉蒂尼子群。所有要考虑的群体都是有限的。
Brauer [1, p. 141] has discussed the question of which subgroups of a group can be determined from its character table. He mentions, referring to p-groups, that the Frattini subgroup can be determined. We show that for an arbitrary finite solvable group, the Frattini subgroup can be determined from the character table. Then we exhibit an infinite set of pairs of non-solvable groups such that both members of a given pair have the same character table but Frattini subgroups of different orders. All groups to be considered are finite.