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#### Mathelogician

##### Member

- Aug 6, 2012

- 35

Here i ask the fisrt serie of questions i couldn't solve;

A basic knowledge of group theory is supposed for solving them!

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1- Can you find 3 subgroups H, k and L of a group G such that H U k U L = G ;and no one of the 3 subgroups is a subgroup of the union of the other 2 subgroups { e.g., H is not a subgroup of (k U L) } ? .... [ In a simpler case assume that G is finite and |H|=|k|=|L|=|G|/2.]

2- Is (R,+) finitely generated? Why?

3- let A,B<G and G be a finite group such that AB is not equal to AB. Then show that |G|>= |A|+|B|.

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Thanks.