| 1. | Standard results about left and right coset spaces then imply the following facts.
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| 2. | As noted earlier, in this case the double coset space equals the right coset space.
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| 3. | If N is normal then gN = Ng implis that every left coset is a right coset.
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| 4. | Conversely, if every left cost is a right coset, then gN = Nh for some h.
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| 5. | Since every right coset is a left coset, there is no need to distinguish " left cosets " from " right cosets ".
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| 6. | As with Thistlethwaite's Algorithm, he would search through the right coset space G _ 1 \ setminus G _ 0 to take the cube to group G _ 1.
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