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thetodd
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Homework Statement
Compute the direct sum Z_12 (+) U(10)
Z_24 is the group Z under addition modulo 12
U(10) is the group Z under multiplication modulo 10
The Attempt at a Solution
I have computed direct sums of Z_n groups before:
For example: Z_2 (+) Z_3 = {(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)}
From this I would think I would follow a similar process but my textbook has the example:
U(8) (+) U(10) = {(1,1),(1,3),(1,7),(1,9),(3,1),(3,3),(3,7),(3,9),(5,1),(5,3),(5,7),(5,9),(7,1),(7,3),(7,7),(7,9)}
What's going on here?
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