## Solution for problem 16.8 Chapter 16

# Consider Z as a subgroup of lR with addition as the operation. Think of the elements of

Modern Algebra: An Introduction | 6th Edition

Consider Z as a subgroup of lR with addition as the operation. Think of the elements of lRas the points on a directed line in the usual way, and then describe the right cosets of Z in lRgeometrically. (Suggestion: Start with a specific example, such as Z + ~.)

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Step 1 of 2

Consider Z as a subgroup ofwith addition as the operation

So, be the group under addition

So, it is geometrically viewed as the horizontal axis

If it is considered to be the group under multiplication, then the entire xy-plane is its picture

is the subgroup of

###### Chapter 16, Problem 16.8 is Solved

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Consider Z as a subgroup of lR with addition as the operation. Think of the elements of