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# State/Cancellation in groups

Proposition: (Cancellation in groups) Suppose that $G$ is a group, and $g,x,y \in G$. Then, if $gx = gy$, then $x = y$. Similarly, if $xg = yg$, then $x = y$.

## Logical Connections

This statement logically relies on the following definitions and statements: Def/Group

The following statements and definitions rely on the material of this page: Def/Group homomorphism, and State/Lagranges theorem

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