I'm quite confused what order of elements consists of. I understand that the order of an element g in a group G is the smallest positive integer n such that g^n = e. And I also understand that to find the order of a group element g, you compute the sequence of products g, g^2, g^3,… until you reach the identity for the first time. The exponenet of this product is the order of g. If the identity never appears in the sequence, then g has infinite order.(adsbygoogle = window.adsbygoogle || []).push({});

For example,

For U(15) = {1,2,4,7,8,11,13,14} under multiplication modulo 15. This group has order 8. To find the order of the element 7, say, we compute the sequence 7^1= 7, 7^2= 4, 7^3= 13, 7^4= 1, so |7|=4. But, how do you find that 1,2,4,7,8,11,13,14 are part of U(15)? if one did not give you the set, how would you be able to find the order of U(15)? or even the order of 7 (|7|)?

A Bigger problem I have,

How do you find order for matrices?

like if A= [0, -1, 1, 0] what is the order of |A|?

Please help!!! I am so confused on how to find order! I reallly appreciate it!! Thanks!

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# Order of Elements!

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