let G be the set of all triples of the form (k1, k2,1) or (k1,k2,-1), where the ki, i=1,2 are integers. define an operation on G by the rule (k1,k2,1) (l1,l2,e)= (k1+l2,k1+l2, e) (k1,k2,-1) (l1,l2,e) = (k1+l2,k2+l1,-e) where e=+1 prove that g is a group. prove that the subgroup h generated by two elements (1,0,1) and (0, 1, 1) is normal in G.

let G be the set of all triples of the form (k1, k2,1) or (k1,k2,-1), where the ki, i=1,2 are integers. define an operation on G by the rule (k1,k2,1) (l1,l2,e)= (k1+l2,k1+l2, e) (k1,k2,-1) (l1,l2,e) = (k1+l2,k2+l1,-e) where e=+1 prove that g is a group. prove that the subgroup h generated by two elements (1,0,1) and (0, 1, 1) is normal in G.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 23E: Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove...

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