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Posted: **Wed May 11, 2022 10:37 pm**

: Problem 1 8 1 Show That Any Subgroup H Of Z G Is Normal In G 2 Let H Be A Subgroup Of Z G And Suppose That G H Is 1 (71.47 KiB) Viewed 11 times

Problem 1.8. 1. Show that any subgroup H of Z(G) is normal in G. 2. Let H be a subgroup of Z(G) and suppose that G/H is cyclic. Show that G is abelian. 3. Let H be a subgroup of Z(G) and suppose that G | H is abelian. Give an example that shows that G is not necessarily abelian.