Intersection-closed subgroup series property

From Groupprops
Jump to: navigation, search

Template:Subgroup series metaproperty


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

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.