Syllabus  MA345
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 JordanHölder Theorem

Soluble and nilpotent groups

Semigroups, machines, flipflop and simple memory machines, flipflop 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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