Existentially bound-word subgroup

Definition
An existentially quantified word-letter pair a pair $$(w,l)$$ where $$w$$ is a word and $$l$$ is a letter used in $$w$$. An element $$g \in G$$ is said to satisfy the pair $$(w,l)$$ if we can find values for the other letters of $$w$$, with $$l = g$$, so that the word $$w$$ simplifies to the identity element. The subgroup corresponding to such a pair is the subgroup generated by all $$g \in G$$ satisfying the pair.

An existentially bound-word subgroup of a group is a subgroup that can be expressed as an arbitrary join of subgroups obtained as finite intersections of subgroups corresponding to existentially quantified word-letter pairs.

Stronger properties

 * Weaker than::Verbal subgroup

Weaker properties

 * Stronger than::Bound-word subgroup
 * Stronger than::Fully characteristic subgroup:
 * Stronger than::Strictly characteristic subgroup