Hypoabelian group

Symbol-free definition
A group is termed hypoabelian if the following equivalent conditions are satisfied:


 * 1) The defining ingredient::perfect core is trivial
 * 2) The defining ingredient::hypoabelianization is the quotient by the trivial subgroup, and hence, isomorphic to the whole group.
 * 3) The transfinite derived series terminates at the identity. (Note that this is the transfinite derived series, where the successor of a given subgroup is its commutator subgroup and subgroups at limit ordinals are given by intersecting all previous subgroups.)
 * 4) There is no nontrivial perfect subgroup.
 * 5) There is a descending transfinite normal series where all the successive quotients are abelian