*Due Thursday Jan. 25*

*In all the problem sets "Ex. C.N" or simply "C.N" stands for the Exercise
from Shoup's book, from Chapter C, number N (in the book they are numbered as "C.N"
as well).*

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- Ex. 1.1
*extra credit: Ex. 1.5*- Prove all the properties listed in Theorem 8.3 for a group (interpreting "+" as the group operation and "-" as the inverse). The commutativity is used only in (iii) and (viii) - restate (iii) in a way that does not require the group to be abelian (for all, except (viii) prove the properties for any groups - abelian or not)
- Ex. 8.2
- For any groups G
_{1}and G_{2}, prove that G_{1}x G_{2}is a group. - Ex. 8.4