Let G act on a non-empty set A. Prove that if a, b E A and...

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Let G act on a non-empty set A. Prove that if a, b E A and b = g.a for some g = G, then Gb = gGag-¹ (Ga is the stabilizer of a). Deduce that if G acts transitively on A then the kernel of the action is ngeGgGag-¹. Let G act on a non-empty set A. Prove that if a, b E A and b = g.a for some g = G, then Gb = gGag-¹ (Ga is the stabilizer of a). Deduce that if G acts transitively on A then the kernel of the action is ngeGgGag-¹.

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Proof Let a and b be two elements in A such that b ga for some g G We need to show that G gGag First ... View the full answer