Can someones tells me how to prove these theorems.(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Lagrange's Theorem (Order of a group) Abstract Algebra

**Physics Forums | Science Articles, Homework Help, Discussion**