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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.
find the value of 0 that makes cos 21 degrees = sin 0 statement true.
Consider the following multiplication in decimal notations: (999).(abc)=def132 ,determine the digits a,b,c,d,e,f. solution) a=8 b=6 c=8 d=8 e=6 f=7 In other words, 999 * 877 = 8
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