Let .

1. The commutator subgroup of I got is .

2. The quotient group of .

Is above 1&2 correct?

Since the maximum order of elements in is 12, the above 2 seems wrong. ((12 * 24!) / (0.5 *24!) = 24 ).

If 2 is wrong, what is the quotient group of 2?

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- Jan 7th 2009, 04:19 AMaliceinwonderlandCommutator subgroup
Let .

1. The commutator subgroup of I got is .

2. The quotient group of .

Is above 1&2 correct?

Since the maximum order of elements in is 12, the above 2 seems wrong. ((12 * 24!) / (0.5 *24!) = 24 ).

If 2 is wrong, what is the quotient group of 2? - Jan 7th 2009, 08:52 AMThePerfectHacker
We need to know that . To prove this just consider a commutator, where and . We can rewrite . But and . Therefore, the subgroup generated by the commutators i.e. is equal to .

Now the commutator subgroup of is (not !) While it is an established result that the commutator of is .

Therefore, I agree with your result. - Jan 7th 2009, 09:41 PMbulls6x
2. is definitely correct. And note that the order of (Z/12)X(Z/2) is 24 not 12. The highest order of a single element is 12 but there are 24 distinct elements in the whole group.