Existentially bound-word 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

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.

Relation with other properties

Stronger properties

Weaker properties