1:Show that union of two subgroups may not be a group?

2:If G is a group and H is a subgroup of index 2 in G,prove that H is normal subgroup of G?

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- Jan 22nd 2009, 12:53 AMMathventureplz solve these problems.....
1:Show that union of two subgroups may not be a group?

2:If G is a group and H is a subgroup of index 2 in G,prove that H is normal subgroup of G? - Jan 22nd 2009, 08:42 AMThePerfectHacker
Take $\displaystyle S_3$ and $\displaystyle <(12)>$ with $\displaystyle <(13)>$.

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2:If G is a group and H is a subgroup of index 2 in G,prove that H is normal subgroup of G?