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Beispiele für die Verwendung von NILPOTENCY in einem Satz

• It follows immediately from any of the above forms of the definition of nilpotency, that the trivial group is the unique group of nilpotency class , and groups of nilpotency class  are exactly the non-trivial abelian groups.
• For a nilpotent group, the lengths of the LCS and the UCS agree, and this length is called the nilpotency class of the group.
• Moreover, every finitely generated nilpotent group G admits a polynomial isoperimetric inequality of degree c + 1, where c is the nilpotency class of G.

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