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Find all subgroups of the Klein 4-Group. How many are there?

Find all subgroups of the Klein 4-Group. How many are there? 1 2 3 4 5 6 7 8 9 10. Find all subgroups of Z 4 . How many are there? 1 2 3 4 5 6 7 8 9 10. What is the first line in this proof? Assume G is an abelian group.

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Find all subgroups of the Klein 4-Group. How many are there?

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  1. Find all subgroups of the Klein 4-Group. How many are there? 1 2 3 4 5 6 7 8 9 10

  2. Find all subgroups of Z4 . How many are there? 1 2 3 4 5 6 7 8 9 10

  3. What is the first line in this proof? • Assume G is an abelian group. • Assume G is a cyclic group. • Assume a * b = b * a.

  4. What is the next line in this proof? • Then G is a subgroup of H. • Then G contains inverses. • Let a, b be any two elements in G. • Let H be any subgroup in G.

  5. What is the last line in this proof? • Thus G is abelian. • Thus H contains inverses. • Therefore H is cyclic. • Then G has primary order.

  6. What is the second to last line in this proof? • Then G is cyclic. • Then G has finite order. • Then H = <?> for some ? in G. • Then H has finite order.

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