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Let <math>G{e,a,b,c}</math> be an abelian group with <math>'e'</math> as an identity element. The order of the other elements are:
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Let <math>G\{e,a,b,c\}</math> be an abelian group with <math>'e'</math> as an identity element. The order of the other elements are:
  
 
(A)2,2,3  
 
(A)2,2,3  

Revision as of 21:54, 9 December 2013

Let <math>G\{e,a,b,c\}</math> be an abelian group with <math>'e'</math> as an identity element. The order of the other elements are:

(A)2,2,3

(B)3,3,3

(C)2,2,4

(D)2,3,4

Solution

* e a b c
e e a b c
a a e b b
b b c e e
c c b e a

a and b have order 2(a * a = e and b * b = e). c has order 4 (since c * c = a and a * a = e)



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Let <math>G\{e,a,b,c\}</math> be an abelian group with <math>'e'</math> as an identity element. The order of the other elements are:

(A)2,2,3

(B)3,3,3

(C)2,2,4

(D)2,3,4

Solution[edit]

* e a b c
e e a b c
a a e b b
b b c e e
c c b e a

a and b have order 2(a * a = e and b * b = e). c has order 4 (since c * c = a and a * a = e)



blog comments powered by Disqus