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

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