any finite integral domain is a field and the order of a finite field is a power of a prime. so (2) is the answer.

<3 + i> is not maximal because it's not prime! (1 + i)(2 - i) is in <3 + i>, but neither 1 + i nor 2 - i are in <3 + i>. so (4) is the answer.

2)which of ideal of the ring Z[i] of gaussian integer is Not maximal?

1)<i+i> ?

2)<1-i>

3)<2+i>

4)<3+i>

every group of order 15 cyclic. we know that if G/Z(G) is cyclic, then G will be abelian, i.e. |G/Z(G)| = 1. so (3) is the answer.

3)if Z(G) denote the center of a group G,then order of quotient group G/G(Z) cannot be

1) 4

2) 6

3) 15

4) 25