| 翻訳と辞書 |
| Perfect core ： ウィキペディア英語版 |
Perfect core
In mathematics, in the field of group theory, the perfect core (or perfect radical) of a group is its largest perfect subgroup. Its existence is guaranteed by the fact that the subgroup generated by a family of perfect subgroups is again a perfect subgroup. The perfect core is also the point where the transfinite derived series stabilizes for any group.
A group whose perfect core is trivial is termed a hypoabelian group. Every solvable group is hypoabelian, and so is every free group. More generally, every residually solvable group is hypoabelian.
The quotient of a group ''G'' by its perfect core is hypoabelian, and is called the hypoabelianization of ''G''.
==References==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Perfect core」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|