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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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