Intersection of finitely many verbal subgroups

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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

Suppose G is a group and H is a subgroup of G. We say that H is an intersection of finitely many verbal subgroups in G if there exists a positive integer n and verbal subgroups H_1,H_2,\dots,H_n of G such that H equals the intersection of subgroups \bigcap_{i=1}^n H_i.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
verbal subgroup generated by a set of words |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
existentially bound-word subgroup |FULL LIST, MORE INFO
fully invariant subgroup invariant under all endomorphisms |FULL LIST, MORE INFO
characteristic subgroup invariant under all automorphisms Fully invariant subgroup|FULL LIST, MORE INFO
normal subgroup invariant under all inner automorphisms Fully invariant subgroup|FULL LIST, MORE INFO