Polynomial Ring - Polynomial Ring. See attached file for full problem description.
Cyclic Groups, Generators and Orders of Elements - (1) Let G be a group such that
...
Show that G cannot be cyclic.
(2) Show that a cyclic group with one generator has at most 2 elements.
(3) Let a 2 G be an element of order two, and b 2 G an ...
Free group proof -
See attached for question.
...Show that F is a free group on S...
Coding Theory : Vectors and Generator Matrices - Please see the attached file for the fully formatted problems.
1(i) Explain what is meant by
(a) a linear code over Fq,
(b) the weight w(u) of a vector u and the distance d(u, v) between vectors ...
Cyclic Group Problem - Let G be a cyclic group of order n.
Show that g^n=1 for all gEG.
If g^m=1 in G where gcd(m,n)=1, show that g=1