Diagonal subgroup of a direct power

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

Suppose $G$ is a group and $H=G^{S}$ is an unrestricted external direct product of $|S|$ copies of $G$. Equivalently, $H$ can be thought of as the group of functions from $S$ to $G$ with the group operations performed pointwise. Then, the diagonal subgroup is the subgroup comprising the constant functions from $S$ to $G$, or equivalently, the elements of $H$ with all coordinates equal.

Relation with other properties

Weaker properties

• Base diagonal of a wreath product