document.write( "Question 1137639: Find all the orders of subroups of Z20?\r
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Algebra.Com's Answer #755478 by ikleyn(52778) $\"\"$ $\"About$

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document.write( "For any subgroup of a group, its order divides the order of the group.\r\n" );
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document.write( "So, we potentially have the orders of subgroups as 2, 4, 5 and 10  (all the divisors of the number 20).\r\n" );
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document.write( "Now, each of these numbers is really realized as the order of a subgroup.\r\n" );
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document.write( "For it, you should know that Z20 is the additive group of integers from 0 to 19 modulus 20.\r\n" );
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document.write( "Then the subgroup of the order 2 is the subgroup (the subset) {0,10} of Z20;\r\n" );
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document.write( "     the subgroup of the order 4 is the subgroup (the subset) {0,5,10,15} of Z20;\r\n" );
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document.write( "     the subgroup of the order 5 is the subgroup (the subset) {0,4,8,12,16} of Z20;\r\n" );
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document.write( "     the subgroup of the order 10 is the subgroup (the subset) {0,2,4,6,8,10,12,14,16,18} of Z20.\r\n" );
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