Relative-intersection-closed subgroup property

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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 property p is termed relative-intersection-closed if it satisfies the following:

Suppose (I, <) is a well-ordered set. Suppose H_i, i \in I is a collection of subgroups of a group G, such that for any i \in I, H_i satisfies property p in some subgroup of G containing both H_i and \bigcap_{j < i} H_j. Then:

\bigcap_{i \in I} H_i

satisfies property p in G.

Relation with other metaproperties

Weaker metaproperties