This article defines a subgroup property modifier (a unary subgroup property operator) -- viz an operator that takes as input a subgroup property and outputs a subgroup property
View a complete list of subgroup property modifiers OR View a list of all subgroup property operators (possibly with multiple inputs)
Given a subgroup property , the large operator applied to the property gives the following subgroup property . A subgroup of satisfes property in if given any subgroup satisfying in :
is trivial is trivial
Some important instances of application of the large operator:
- large subgroup: obtained from the tautology subgroup property
- normality-large subgroup: obtained from normal subgroup
Note that the property of being large with respect to says something like: for every subgroup with property . Thus, the more subgroups there are with property , the harder it is to be -large. More formally if , then -large -large.