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Determine the centralizer and the order of the conjugacy:
1) Determine the centralizer and the order of the conjugacy class of the matrix [1, 1; 0, 1] in Gl2(F3).
2) Prove that the icosahedral group has a subgroup of order 10.
3) Let G be a group of order n which acts nontrivially on a set of order r. Prove that if n>r!, then G has a proper normal subgroup.
4) Determine the conjugacy classes in the dihedral group D10 and write down the class equation for this group. Find the center of D10.
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Q1: Find three positive numbers whose sum is 54 and whose product is as large as possible.
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What is the lesser of two consecutive positive integers whose product is 90? Let x = the lesser integer and let x + 1 = the greater integer. Because product is a key word for m
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