CS-235. Problem Set 1
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"
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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 G1 and G2, prove that
G1 x G2 is a group.
- Ex. 8.4