Daniel HW2

12.1 c cannot be an equivalence relation since it fails reflexivity. Consider (pi, pi). 2 pi is not rational. The other choices were correct. 12.2. Good catches! 12.7. Good. 11.3. Great! Very rigorous: Thanks for making sure you were consider the non-identity (so order > 1(. Just need to cite Lagrange's theorem whenever you use it. 11.4. Spot on direct application of Lagrange's theorem. 11.12. Julian used a different approach when attacking this problem with Cauchy's Theorem (his homework is posted on the main website). How do we know the order of the group is a power of a prime number (In fact, R_11 has 10 elements).

Hm..kinda got lost at this point:

"p1^a1,p2^a2…pk^ak are included in determining the size of m" m is the order of the group, but what are the a_i's and p_i's?

" Then I can state, that by theorem 20.1; the first sylow theorem. If p^s for an arbitrary p divides k1" What is k_1?