so i'm solving problems that tell me to find the left cosets, but I dont really know what they are.(adsbygoogle = window.adsbygoogle || []).push({});

by defn, let G be a group and H a subgp of G.. and let a be an element of G. the set ah for any h in H, denoted by aH is the left coset.

I mean, what does that mean. so for an example problem. find the left cosets of {1, 11} in U(30). So U(30) has order 8, with elements 1 7 11 13 17 19 23 29. By formula, order of G/H equalis the number of left cosets. so 8/2 = 4. meaning we have 4 left cosets. and the book says the cosets are H 7H 13H and 19H.

so exactly why? what are those numbers? how did they derive that?

at first, I thought you just take each element and multiply by H, , so aH = 1H, 3H, 7H.......29H,but I guess I was way off.

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# Homework Help: What are cosets?

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