Subgrpous

Prove: any subgroup of the order of p^(n-1) in a group of order p^n, where p is a prime, is a normal subgroup

Integral domain

There is integral domain with exactly six elements. Disprove or Prove

Algebraic numbers

Is sin 1 degree an algebraic number?

Transformations in Hom(v,v)

Prove that the invertible transformations in Hom(v,v) form a group under multiplication

Automorphism

1. Let T be any automorphism of G, show that ZT<(subset) Z. If G is a group and Z is the center of G.