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

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Advance Math

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

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

Theorem 3.14 - f H ? G and [G: H] = n, then there is ahomomorphism ?: G -> Sn with ker ? ? H.

Theorem 3.17 - Let H ? G and let X be the family of all theconjugates of H in G. There is a homomorphism ?: G ->Sx with ker ? ? NG(H).

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