Question

(5)(20 points) In the problems below, give the order of the element in the indicated factor group. (a) (1, 2)+ < (1,1) > in ZIn the problems below, give the order of the element in the indicated
factor group.
(a)  in

(b)  in

(c)  in

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Answer #1

(1,2) 7 <11,97 in Zzc761 <(1,12 Note The order of this element is the smallest positive integer k for which k( 1,2) + <0,1))(3,2+ < 4,4 > In 26+ 20 / cala7 to Pud k such that k c (3, 2) + < (4,4))) = (6,0) PC (4937 26.04%, In Nole 24,47 003) 4 0(2)D to find onder y 26 t <12> In 260/2127 The Smeelest positiu order of this element is the integer K. for Wheen k (264 <1,2>)

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