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 propertyTemplate:Transiter
View a complete list of subgroup property modifiers OR View a list of all subgroup property operators (possibly with multiple inputs)
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Let be a subgroup property. Then the join-transiter of is the property of being a subgroup such that its join with any subgroup having property again has property in the whole group.
Definition with symbols
Let be a subgroup property. Then the join-transiter of is the property such that: A subgroup has property in if and only if whenever has property , has property in .