Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
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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=== | ||
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
| * | 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
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
| * | 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
GATECSE