Intersection-closed subgroup series property

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Definition

Symbol-free definition

A subgroup series property is said to be intersection-closed if the intersection of any two subgroup series, both having the property, also has the property. Here, by intersection of subgroup series, we mean the member-wise intersection.

Definition with symbols

A subgroup series property $p$ is said to be intersection-closed if whenever $S$ and $S'$ are two subgroup series, each having property $p$ so does $S\cap S'$.

Related notions

A related notion to this is series-intersection-closed subgroup property, viz a subgroup property wherein the property of being a subgroup series wherein each member satisfies the property in its successor, is an intersection-closed subgroup series property.