division algorithm in group theory

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leekitah
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division algorithm in group theory

Post by leekitah » Sat Mar 30, 2013 3:22 am

How to use division algorithm in group theory? Could any mathematicians out there guide me through either (or both preferably) of the following questions:
Use the notion of a greatest common divisor or the division algorithm in
Z to show that every subgroup of Z has the form mZ := (mk : k e Z)
for some m e Z.
Show (using the division algorithm for integers) that if G = (g) is a
cyclic group of order n, then g^t = e for some t e Z if n divides t.
Any help would be greatly appreciated.

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