Question

Let G = ?12, which is a group under addition modulo 12, and let H = ?3? ? G. (a) Apply Lagrange's Theorem to compute the number of elements of G/H, without actually calculating those elements. (b) Now, list the elements of G/H. List each one only once, and for each element, identify it both by a name like a + H and by writing the elements within a + H. (c) Make a table that shows how to add any two elements of the group G/H. (d) To which familiar group is G/H isomorphic? Write down an explicit isomorphism between G/H and this group.

          Let G = ?12, which is a group under addition modulo 12, and let
H = ?3? ? G.
(a) Apply Lagrange's Theorem to compute the number of elements of G/H, without actually calculating those elements.
(b) Now, list the elements of G/H. List each one only once, and for each element, identify it both by a name like a + H and by writing the elements within a + H.
(c) Make a table that shows how to add any two elements of the group G/H.
(d) To which familiar group is G/H isomorphic? Write down an explicit isomorphism between G/H and this group.

Let G = ?12, which is a group under addition modulo 12, and let
H = ?3? ? G.
(a) Apply Lagrange's Theorem to compute the number of elements of G/H, without actually calculating those elements.
(b) Now, list the elements of G/H. List each one only once, and for each element, identify it both by a name like a + H and by writing the elements within a + H.
(c) Make a table that shows how to add any two elements of the group G/H.
(d) To which familiar group is G/H isomorphic? Write down an explicit isomorphism between G/H and this group.

Added by Kaitlyn C.

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