Join-transiter

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)

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Definition

Symbol-free definition

Let $p$ be a subgroup property. Then the join-transiter of $p$ is the property of being a subgroup such that its join with any subgroup having property $p$ again has property $p$ in the whole group.

Definition with symbols

Let $p$ be a subgroup property. Then the join-transiter of $p$ is the property $q$ such that: A subgroup $H$ has property $q$ in $G$ if and only if whenever $K\leq G$ has property $p$, $<H,K>$ has property $p$ in $G$.