Course: MAT 351 3.0 Group Theory (Compulsory)
Course Content:
Definitions and Examples of Groups, Commutative and non-commutative groups, The group of integers modulo n (Zn ), Subgroups, Lagrange’s Theorem, Homomorphisms and Normal Subgroups, Factor Groups, The Homomorphism Theorems, Cyclic Groups, Symmetric, Alternating and Dihedral Groups, Group Actions, Direct Products and Sums, Conjugacy classes, Cauchy theorem and p-groups, Sylow Theorems, Free Groups, Free Abelian groups, Finitely generated Abelian groups, Classification of Finite groups, Nilpotent and Solvable Groups, Normal and Subnormal Series.
Recommended Readings:
- Dummit, D. S., & Foote, R. M. (2004). Abstract algebra. Hoboken: Wiley.
- Herstein, I. N. (1975). Topics in algebra. New York: Wiley.
- Baumslag, B., & Chandler, B. (1968). Group theory. New York: McGraw-Hill.
- Fraleigh, J. B. (1982). A first course in abstract algebra. Reading, Massachusetts: Addison-Wesley.
- Malik, D. S., Mordeson, J. M., & Sen, M. K. (1997). Fundamentals of abstract algebra. New York: The McGraw-Hill Companies.
- Hungerford, Thomas W. (1980). Algebra. New York: Springer-Verlag.