Definition: Group Operation
Let \((G,\circ)\) be a group and let \(M\) be a set. A function \[\circ:\cases{G\times M\longrightarrow M,\cr (g,x)\longmapsto g\circ x},\]
is called a group operation (of \(G\) on \(M\)), if the following properties are fulfilled:
- \(e\circ x=x\) for all \(x\in M\).
- \((g\circ h)\circ x=g\circ (h\circ x)\) for all \(g,h\in G\) and for all \(x\in M\).
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References
Adapted from CC BY-SA 3.0 Sources:
- Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück
