Decomposable group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

Symbol-free definition

A group is called decomposable if it is the internal direct product of two of its proper subgroups.

Symbolic definition

Let $G$ be a group. $G$ is called decomposable if there exist subgroups $H,K\leq G$ such that $\{e\}\neq H,K$, $G=H\times K$.