Difference between revisions of "Abelian Group"

Revision as of 22:26, 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

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

@@ Line 7: / Line 7: @@
 (C)2,2,4
-'''(D)2,3,4'''
+'''(D)2,4,4'''
 ===Solution===
@@ Line 44: / Line 44: @@
 |}
-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)
+ 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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