Let G be a group of permutations on a set X. Let a ∈ X and define stab(a) 5 { α ∈ G | α (a) 5 a}. We call stab(a) the stabilizer of a in G (since it consists of all members of G that leave a fixed). Prove that stab(a) is a subgroup of G. (This subgroup was introduced by Galois in 1832.) This exercise is referred to in Chapter 7.
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