Unformatted text preview: Exercise 4. Let G be a group in which every element has order less than or equal to 2. Show that G is abelian. [ Hint: Consider ( ab ) 2 for arbitrary a,b ∈ G .] Exercise 5. The exponent of a group G is the smallest n ∈ N so that a n = e for all a ∈ G . a. Show that the exponent of G is the least common multiple of the orders of the elements in G . b. Find the exponents of S 3 ,S 4 and S 5 ....
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- Spring '10
- Algebra, Elementary algebra, σ, Binary operation