# Group with subgroups proof

1. Mar 30, 2009

### kathrynag

1. The problem statement, all variables and given/known data

Let G be a group with subgroups H and K. Prove HintersectK is a subgroup.

2. Relevant equations

3. The attempt at a solution
G is a group with subgroups H and K. Then H and K are closed, have identity elements in G and have inverses.
HintersectK is a subgroup because H and K must satisfy the same properties of G.

2. Mar 30, 2009

### NJOsment

let $$a,b \epsilon H$$ and $$a,b \epsilon K$$.Then $$a*b \epsilon H$$ and $$a*b \epsilon K$$.Let $$a \epsilon H$$ and $$a \epsilon K$$.Then $$a^{-1} \epsilon H$$ and $$a^{-1} \epsilon K$$.

3. Mar 30, 2009

### kathrynag

that makes sense