In mathematics, in the field of group theory, the perfect core (or perfect radical) of a group is its largest perfect subgroup.[1] 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.
^Wan, Zhexian; Shi, Sheng-Ming (1996). Group Theory in China. Springer Science & Business Media. p. 23. ISBN 9780792339892. Retrieved 1 August 2018.
mathematics, in the field of group theory, the perfectcore (or perfect radical) of a group is its largest perfect subgroup. Its existence is guaranteed by...
Perfect Blue (Japanese: パーフェクトブルー, Hepburn: Pāfekuto Burū) is a 1997 Japanese anime psychological thriller film directed by Satoshi Kon. It is loosely...
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obtaining the transfinite derived series, which eventually terminates at the perfectcore of the group. Given a group G {\displaystyle G} , a quotient group G...
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cutter (also called a core drill, core cutter, broach cutter, trepanning drill, hole saw, or cup-type cutter) is a form of core drill used to create holes...
the order of every element. perfectcore The perfectcore of a group is its largest perfect subgroup. perfect group A perfect group is a group that is equal...
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