# Join operator

From Groupprops

*This is a binary subgroup property operator, viz an operator that takes as input two subgroup properties, and outputs one subgroup property*Template:Property existentialization

## Contents |

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

## Definition

### Definition with symbols

Given two subgroup properties and , the join of and , denoted as , is defined as follows: a subgroup satisfies property in if there exist subgroups of such that satisfies in , satisfies in , and .