Groups of order 32: Difference between revisions
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| [[Direct product of Q8 and V4]] || 47 || || 1 || 7 || 24 || 0 || 0 || 0 | | [[Direct product of Q8 and V4]] || 47 || || 1 || 7 || 24 || 0 || 0 || 0 | ||
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| [[SmallGroup(32,48)]] || 48 || | | [[SmallGroup(32,48)]] || 48 || || 1 || 15 || 16 || 0 || 0 || 0 | ||
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| [[Inner holomorph of D8]] || 49 || || 1 || 19 || 12 || 0 || 0 || 0 | | [[Inner holomorph of D8]] || 49 || || 1 || 19 || 12 || 0 || 0 || 0 | ||
Revision as of 16:50, 31 May 2010
The list
Element structure
Order statistics
FACTS TO CHECK AGAINST:
ORDER STATISTICS (cf. order statistics, order statistics-equivalent finite groups): number of nth roots is a multiple of n | Finite abelian groups with the same order statistics are isomorphic | Lazard Lie group has the same order statistics as the additive group of its Lazard Lie ring | Frobenius conjecture on nth roots
1-ISOMORPHISM (cf. 1-isomorphic groups): Lazard Lie group is 1-isomorphic to the additive group of its Lazard Lie ring | order statistics-equivalent not implies 1-isomorphic
Note that because number of nth roots is a multiple of n, we see that the number of elements whose order is or is odd, while all the other numbers are even. The total number of roots is even for all .