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On Alperin’s fusion theorem. (English) Zbl 0837.20028
The author gives a graph theoretical interpretation of Alperin’s known theorem on the fusion of $$p$$-elements in a finite group and its variations by Alperin, Gorenstein and Goldschmidt. Then he uses this interpretation to give a simple proof of a result generalizing all theorems mentioned.

##### MSC:
 20D20 Sylow subgroups, Sylow properties, $$\pi$$-groups, $$\pi$$-structure 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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