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Unformatted text preview: H of an abelian group G , the cosets of H in G actually form a subgroup themselves. The operation is given by ( aH )( bH ) = ( ab ) H . Thus, the easiest way to gure out the cosets of the subgroup H generated by [7] in U 19 is to compute H, [2] H, [4] H, [8] H,. .. (powers of [2] H ) until one gets H back ( H is the identity in the coset group). Lagranges theorem tells us the number of distinct cosets. For H = < [7] > , the six (  G   H  = 18 3 = 6) cosets H, [2] H, [4] H, [8] H, [16 H ] , [32] H = [13] H are all distinct....
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 Spring '08
 BILLERA
 Math, Algebra, Addition

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