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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.
The square of one integer is 55 less than the square of the next consecutive integer. Find the lesser integer. Let x = the lesser integer and let x + 1 = the greater integer. T
what is the lowest term of 11/121
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what are the formulas in finding the perimeter of a plane figure?
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