1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 h^11 h^21 Free CICY quotients, Resolutions of ...
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1or3. EverythinginZ3 has order 1 or 3, so a can be any element in Z3.InZ9,thereare (9) = 323=6elementsoforder9.Thusthereare3*6=18elementsoforder9inZ 3Z9. #13: Foreachintegern>1, give two examples of two non isomorphic groups of order n2. Z n2 and Z Z (Note: we know these are di↵erent since n is not relatively prime to n.) # 14: The dihedral ...

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• Jul 04, 2010 · GAP implementation Group ID. This finite group has order 27 and has ID 2 among the groups of order 27 in GAP's SmallGroup library. For context, there are groups of order 27. It can thus be defined using GAP's SmallGroup function a

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z / 21 z, z / 15 z, z / 2 z ⊕ z / 14 z, and z / 3 z ⊕ z / 9 z which occur for 4,2,2, and 1 Q ¯ ‐isomorphism classes, respectively. The proof of Theorem 1.7 gives a concrete demonstration of the general strategy for determining the torsion subgroups for curves which have been base‐extended to Q ( G ∞ ) for more general G .

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Your solution is right. As, I am noting that(may be i'm wrong), you are applying that "A cyclic subgroup of order \$4\$ must contain \$2\$ elements of order \$4\$ and \$1\$ element of order \$2\$, and you searching those elements and listing them.

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look under multiplication, and go thru all numbers. See if any of them cycles thru all of 1-12 as you multiply repeatedly. For example 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1 so 2 is a generator and z13 is cyclic under multiplication

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