Arjun Suresh (talk | contribs) |
Arjun Suresh (talk | contribs) |
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| Line 5: | Line 5: | ||
(B)3,3,3 | (B)3,3,3 | ||
| − | + | (C)2,2,4 | |
| − | (D)2,3,4 | + | '''(D)2,3,4''' |
===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)2,3,4
| * | 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)
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
| * | 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)
GATECSE