Order of element in a group
(Monday, May 3, 2010)
Definition
Let áG, *ñ be a group and let a e G, then the lease positive integer n, if it exists, such that an=e is called the order of the element a and is denoted by O(a) = n.
Note: (i) If n does not exist, then we say that a is of infinite or zero order
(ii) O(e) = 1, since e1 = e.
Example 1
Find the order of the elements in the multiplicative group G = {1, -1, i, -i}
Solution:
O(1) = 1, since 11 = 1
O(-1) = 2, since (-1)2 = 1
O(i) = 4, since i4 = 1
O(-i) = 4, since (-i)4 = 1
Posted in Posted by waytofeed at 7:51 AM
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