 Nilpotency class of a direct product (source code)

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= Nilpotency class of a direct product
{title2=$c(A\times B)=\max\{c(A),c(B)\}$}

<Group commutators> are taken coordinatewise in a <direct product of groups>, giving $\Gamma_j(A\times B)=\Gamma_j(A)\times\Gamma_j(B)$. A finite direct product of <nilpotent groups> is nilpotent, with class the maximum of the factor classes.

// Target: algebra.bigb

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