An Introduction of the Theory of Groups - Fourth Edition (Joseph J. Rotman) If H ≤...

An Introduction of the Theory of Groups - Fourth Edition (Joseph J. Rotman)

If H ≤ G, then show that G acts transitively on the set of all left cosets of H (Theorem 3.14) and G acts transitively on the set of all conjugates of H (Theorem 3.17).

Theorem 3.14 - f H ≤ G and [G: H] = n, then there is a homomorphism ρ: G -> Sn with ker ρ ≤ H.

Theorem 3.17 - Let H ≤ G and let X be the family of all the conjugates of H in G. There is a homomorphism ψ: G -> S_x with ker ψ ≤ N_G(H).

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Colby Messinger answered 1 year ago

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