Crystallographic Group: Relationship to A5 Group

Can the group A5 be a subgroup of the rotation group in a three dimentional crystallographic group?

Conjugacy classes

Please see the attached PDF file.

Describe the Rings

Please see the attached file for the fully formatted problem. Describe the rings: Z[x]/(x2-3, 2x+4),Z[i]/(2+i)

Describe the Ring.

Please see the attached file for the fully formatted problem. Describe the ring obtained from Z12 by adjoining the element 1/2 (the inverse of 2).

Rings : Integral Domain

Is there an integral domain containing exactly 10 elements? Show that any finite ring which is an integral domain is in fact a field.

Rings : Fields

Please see the attached file for the fully formatted problems. Prove that Z5/(x2 + x + 1) is a field. How many elements are there in this field? Can you also represent it as Z5[x]/(x2-a) where a is some element of Z5?

Rings

Please see the attached file for the fully formatted problems. Describe the rings: Z[x]/(x2 - 3, 2x + 4), Z[i]/(2 + i)

Rings : Elements

Please see the attached file for the fully formatted problems. Describe the ring obtained from Z12 by adjoining the element 1/2 (the inverse of 2).

Find Irreducible Polynomial

Find an irreducible polynomial defining the extension Q(3^1/2, 5^1/2).

Galois Groups of Irreducible Polynomials

Describe all subgroups of S5 which are Galois groups of irreducible polynomials of degree 5.