Let H and K be groups with relatively prime orders. Show that Aut(HxK)≃ Aut(H)xAut(K).
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Originally Posted by henderson7878 Let H and K be groups with relatively prime orders. Show that Aut(HxK)≃ Aut(H)xAut(K). Given and , define a map by . Show that this is a well defined homomorphism first, then show that it is bijective.
Hi, This really isn't very hard, but it is kind of messy. The previous answer is a little misleading in that it looks as though Aut(H) cross Aut(K) would always be isomorphic to Aut(H cross K), which of course is false. Here's the mess:
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