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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:
 
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  
  
(B)3,3,3  
+
(B) 3,3,3  
  
(C)2,2,4  
+
(C) 2,2,4  
  
'''(D)2,4,4'''
+
'''(D) 2,4,4'''
  
 
===Solution===
 
===Solution===

Revision as of 22:29, 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) 2,4,4

Solution

* e a b c
e e a b c
a a e c b
b b c a e
c c b e a
a * a = e => order(a) = 2
b * b * b * b = a * b * b = c * b = e => order(b) = 4
c * c * c * c = a * c * c = b * c = e => order(c) = 4



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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) 2,4,4

Solution[edit]

* e a b c
e e a b c
a a e c b
b b c a e
c c b e a
a * a = e => order(a) = 2
b * b * b * b = a * b * b = c * b = e => order(b) = 4
c * c * c * c = a * c * c = b * c = e => order(c) = 4



blog comments powered by Disqus