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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,
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- (Ga is the stabilizer of a). Deduce that if G acts transitively on A then the kernel of the action is ngeGgGag-.
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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 ...
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Discrete and Combinatorial Mathematics An Applied Introduction
Authors: Ralph P. Grimaldi
5th edition
201726343, 978-0201726343
