Nilpotency of fixed class is quotient-closed

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This article gives the statement, and possibly proof, of a group property (i.e., nilpotent group) satisfying a group metaproperty (i.e., quotient-closed group property)
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Statement

Suppose G is a nilpotent group and H is a normal subgroup of G and G/H is the corresponding quotient group. Then, G/H is also a nilpotent group and its nilpotency class is at most equal to the nilpotency class of G.

Note that we say that a group is nilpotent "of class c" if its nilpotency class is at most c. The statement can thus be reformulated as saying that the property of being nilpotent of class c is closed under taking quotients.

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