MA343 Group Theory (part one)

• Group axioms, cyclic groups, permutation groups.
• Normal subghroups, homomorphisms, isomorphism theorems.
• Permutation groups, isomorphism theorems, linear groups
• Direct and semidirect products
• Finitely generated Abelian groups
• Automorphisms, groups of automorphisms

MA344 Group Theory (part two)

• Group actions, automorphism groups of graphs, application to enumeration.
• Sylow's Theorem, groups of small order
• Simple groups, the Jordan-Hölder Theorem
• Soluble and nilpotent groups
• Semigroups, machines, flip-flop and simple memory machines, flip-flop with reset

References

• J.B. Fraleigh, "A First Course in Abstract Algebra" (Addison Wesley)
• W. Ledermann, "Introduction to the Theory of Finite Groups" (Oliver & Boyd)
• I.D. Macdonald, "The Theory of Groups" (Oxford)
• J.S. Rose, "A Course on Group Theory" (Cambridge)

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