Base (group theory)

Let ${\displaystyle G}$ be a finite permutation group acting on a set ${\displaystyle \Omega }$. A sequence

of k distinct elements of ${\displaystyle \Omega }$ is a base for G if the only element of ${\displaystyle G}$ which fixes every ${\displaystyle \beta _{i}\in B}$ pointwise is the identity element of ${\displaystyle G}$.

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