Group Theory (LVI): Prove that the centre of a group is always a normal subgroup.

Modern Algebra Group Theory (LVI) Normal Subgroups of a Group Centre of a Group Prove that the centre of a group is always a normal subgroup.

Group Theory (LVII): A group of order p^2,where p is a prime number, is abelian.

Modern Algebra Group Theory (LVII) A Group of Order p^2, where p is a prime Normalizer or Centralizer of an element of a Group Abelian Group A group of order p^2,where p is a prime number, is abelian.

Group Theory (LVIII): Prove that a group of order 9 is abelian.

Modern Algebra Group Theory (LVIII) A Group of Order p^2, where p is a prime Normalizer or Centralizer of an element of a Group Abelian Group Prove that a group of order 9 is abelian.

Group Theory (LIX): Quotient Group or Factor Group: If G is abelian and if N is any subgroup of G, prove that G/N is abelian.

Modern Algebra Group Theory (LIX) Quotient Group or Factor Group Abelian Group If G is abelian and if N is any subgroup of G, prove that G/N is abelian.

Group Theory (LXI): Automorphism of a Group: Is the mapping given below an automorphism of the group ? G group of integers under addition, T:x→ -x

Modern Algebra Group Theory (LXI) Automorphism of a Group Is the mapping given below an automorphism of the group ? G group of integers under addition, T:x→ -x