MT305 - Group Theory
Sorry !. MT305 not offered in current semester.
Credits: 3 Credits
Recall of Basic Group Theory: Groups, Dihedral, symmetric, alternating, icosohedral and cyclic groups, generators and relations, subgroups, cosets, normal subgroups, quotient groups, group homomorphisms, isomorphism theorems, lattice isomorphism theorem. Group Actions: Definitions, orbits and stabilizers, permutation representations, groups acting on themselves by left multiplication and conjugation, Cayley's Theorem, class equation, groups acting on groups. Automorphisms: Sylow's Theorem, Applications of Sylow's theorem, p-groups, Theorems to groups of medium order, simple groups, simplicity of $A_n$ for $n>4$. Series of Groups: Subnormal and Normal Series, Jordan-Holder Theorem, Solvable and nilpotent groups, Non-solvability of $S_n$ for $(n>4)$