Unformatted text preview: G . Let n =  H  be the number of elements in H . Prove that H contains the identity element. M.3 (8 points) For this question, you may assume any theorems or facts from lecture. (a) (4 points) What is the last digit of 1983 21 ? Prove that your answer is correct. (b) (4 points) What are the last two digits of 1983 41 ? M.3 1 2 (0 points) What was Euler’s ﬁrst name? Prove it. M.4 (10 points) Let G be an arbitrary group. (a) (5 points) Prove that for any element a ∈ G , aG = G . (b) (5 points) Suppose G is a ﬁnite group, and consider its multiplication table. Using (a) or otherwise, explain why the same element of G cannot appear twice in the same row of the table. 1...
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 Fall '10
 GideonMaschler
 Addition, Integers, Natural number, Mississauga Department of Mathematical and Computational Sciences, Leo Goldmakher

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