Join operator

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

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Definition with symbols

Given two subgroup properties p and q, the join of p and q, denoted as \langle p,q \rangle, is defined as follows: a subgroup H satisfies property \langle p, q \rangle in G if there exist subgroups K_1,K_2 of H such that K_1 satisfies p in G, K_2 satisfies q in G, and H = <K_1,K_2>.