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Proposition: Unique Solvability of $a\ast x=b$ in Groups

In every group $(G,\ast),$ the equation \(a\ast x=b\) is uniquely solvable for all $a,b\in G$ and its solution is $x=a^{-1}\ast b$ where $a^{-1}$ is the inverse element of $a$ in $G.$

Table of Contents

Proofs: 1

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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983