Courses :: Module, GROUP THEORY 1

	Overview
	A rigorous introduction to Group Theory. Group Axioms and examples of groups. Direct products. Cyclic groups. The symmetric groups. Subgroups and Lagrange's Theorem. Conjugacy and the class equation. Normal subgroups, quotient groups. Homomorphisms, isomorphisms, the First Isomorphism theorem, the correspondence theorem. Cayley's Theorem. The classification of finitely generated Abelian groups.

Overview

A rigorous introduction to Group Theory. Group Axioms and examples of groups. Direct products. Cyclic groups. The symmetric groups. Subgroups and Lagrange's Theorem. Conjugacy and the class equation. Normal subgroups, quotient groups. Homomorphisms, isomorphisms, the First Isomorphism theorem, the correspondence theorem. Cayley's Theorem. The classification of finitely generated Abelian groups.

	Learning Outcomes
	On successful completion of the module, students should be able to: State the axioms defining a group and any definitions or theorems given in the course. Decide whether given examples satisfy these definitions. Prove results using definitions and theorems given in the course. Perform calculations in a group theoretic setting. Give examples which illustrate concepts from the course. State, prove and apply some of the classical theorems of elementary Group Theory.

Learning Outcomes

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes Continuous assessment mark is carried forward to the Autumn. University scheduled written examination (Autumn): 120 minutes, On-campus

Autumn Supplementals/Resits

	Pre-Requisites
	(MT241P and MT242P) or MT216C/MT212A. Equivalent modules would also suffice.

Pre-Requisites

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Courses / Module

GROUP THEORY 1

Semester 1

Semester 2