Perfect core
From HandWiki
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.
References
- ↑ Wan, Zhexian; Shi, Sheng-Ming (1996) (in en). Group Theory in China. Springer Science & Business Media. p. 23. ISBN 9780792339892. https://books.google.com/books?id=VLhj4v7kVxwC&dq=%22perfect+radical%22+group+theory&pg=PA23. Retrieved 1 August 2018.
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