(New page: |<math>Z_12\oplus Z_4\oplus Z_15</math>| = lcm(12,4,15) =60. Let G = <math>Z_12\oplus Z_4\oplus Z_15</math>, and H be a subgroup of G with |H|=9. By Lagrange's theorem, if H is a subgroup ...) |
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Revision as of 18:19, 8 October 2008
|$ Z_12\oplus Z_4\oplus Z_15 $| = lcm(12,4,15) =60. Let G = $ Z_12\oplus Z_4\oplus Z_15 $, and H be a subgroup of G with |H|=9. By Lagrange's theorem, if H is a subgroup of G, then |H| divides |G|; however, 9 does not divide 60, therefore there is no such subgroup.
