Let G ≤ S n {\displaystyle G\leq S_{n}} be a permutation group. Let B = ( β 1 , β 2 , … , β r ) {\displaystyle B=(\beta _{1},\beta _{2},\ldots ,\beta _{r})} be a sequence of distinct integers, β i ∈ { 1 , 2 , … , n } {\displaystyle \beta _{i}\in \{1,2,\ldots ,n\}} , such that the pointwise stabilizer of B {\displaystyle B} is trivial. Define B i = ( β 1 , β 2 , … , β i ) {\displaystyle B_{i}=(\beta _{1},\beta _{2},\ldots ,\beta _{i})} , and define G ( i ) {\displaystyle G^{(i)}} to be the pointwise stabilizer of B i {\displaystyle B_{i}} . A strong generating set for the base B {\displaystyle B} is a set S ⊂ G {\displaystyle S\subset G} such that ⟨ S ∩ G ( i ) ⟩ = G ( i ) {\displaystyle \langle S\cap G^{(i)}\rangle =G^{(i)}} for each 1 ≤ i ≤ r {\displaystyle 1\leq i\leq r} .
