Fixed-class tuple fraction

From Groupprops
Jump to: navigation, search


Suppose G is a finite group and c is a positive integer. Define the set:

CT_c(G) = \{ (x_1,x_2,\dots,x_{c+1}) \in G^{c+1} \mid [[ \dots [x_1,x_2],x_3],\dots,x_c],x_{c+1}] = e \}

Then, the class c tuple fraction of G is defined as:


Note that this fraction equals 1 if and only if G is a nilpotent group of nilpotency class at most c.