Potentially iterated commutator subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup H of a group G is termed a potentially iterated commutator subgroup of G if there exists a group K containing G such that H is an iterated commutator subgroup of K, i.e., H is obtained from K through a series of operations that involve taking the commutator of two subgroups. (special cases of this are when H is in the finite part of the derived series or the lower central series of K).

Formalisms

In terms of the potentially operator

This property is obtained by applying the potentially operator to the property: iterated commutator subgroup
View other properties obtained by applying the potentially operator

Relation with other properties

Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Iterated commutator subgroup

Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Normal subgroup |FULL LIST, MORE INFO
Solvable-quotient normal subgroup |FULL LIST, MORE INFO