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anna010101

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1. Prove that if G is a group of order p^2 (p is a prime) and G is not cyclic, then a^p = e (identity element) for each a E(belongs to) G.

2. Prove that if H is a subgroup of G, [G]=2, a, b E G, a not E H and b not E H, then ab E H.

3. Verify that S4 has at least one subgroup of order k for ech divisor of 24

4. If H is a subgroup of G and [G] = 2, the the right cosets of H in G are the same as the left cosets of H in G. Why?

5. Prove that if H is a subgroup of a finite grup G, the n the number of right cosets of H in G equals the number of left cosets of H in G.

Also, does anyone know a good website that has good information for abstract algebra. Thanks.