Question

Abstract Algebra

I need help on a problem that requires the definition of Cosets.

The definition is given in the given picture as well as the problem above it.

Step 1

Given *H = <5> = {n∈ Z | n = 5m,* for some integer *m*}.

The left cosets will be:

0 + H, 1 + H, 2 + H, 3 + H, 4 + H,... and in general *a + H,* where *a* is any integer.

Step 2

To find the distinct left cosets.

Step 3

To list the 5 distinc...

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