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In abstract algebra, especially in the area of group theory, a strong generating set of a permutation group is a generating set that clearly exhibits the permutation structure as described by a stabilizer chain. A stabilizer chain is a sequence of subgroups, each containing the next and each stabilizing one more point.
Let G ≤ S n {\displaystyle G\leq S_{n}} be a group of permutations of the set { 1 , 2 , … , n } . {\displaystyle \{1,2,\ldots ,n\}.} Let
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
and define G {\displaystyle G^{}} to be the pointwise stabilizer of B i {\displaystyle B_{i}}. A strong generating set for G relative to the base B {\displaystyle B} is a set