Let I denote the field generated by x^4+x^3+x^2+x+1 in Z2[x] and F=Z2[x]/I then
.1)F is an infinite field
2)F is finite field with 4 elements
3)F is finite field with 8 elements
4)F is finite field with 16 elements
next question
let G be k group with the generators a and b given by
G= <a,b:a^4=b^2=1,b2=(a^-1)b>
if Z(G) denote the center of G then G/Z(G) is isomorphic to
1)the trivial group
2)C2,the cyclic group of order 2
3)C2 x C2
4)C4
please please explain the answer these questions were asked by indian institue of technology delhi
in gate entrance exam