Groups:
Definition of a group
Subgroup
Subgroup generated by a set
The cyclic groups, cosets
Lagrange’s theorem
Normalizer centralizer.
The center of a group.
Equivalence relation in a group
Conjugacy classes
Normal subgroups
Quotient group.
Group homomorphisms
Homomorphisms
Isomorphism
Automorphism.
Kernel and image of homomorphism.
Isomorphism theorems.
Permutation groups.
The cyclic decomposition of a permutation group.
Cayley’s theorem.
Direct product of two groups and examples.
