## Module details 2017–18

Full details of all undergraduate modules offered by the School of Mathematical Sciences for 2017–18. Module organisers that have changed from last year are indicated by a * after their names. You may find it easier to view this information if you click on the Zoom button towards the top right of the page. Beware that the list of all modules is somewhat slow to download.

Previous module details are available in the archive of module details from previous years. You can access timetables via QMplus and via the Queen Mary central web timetables, even when QMplus module pages are hidden.

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UG code: MTH714U
Module name:
Description:

This module provides an introduction to advanced group theory. The aim is to explore the theory of finite groups by studying important examples in detail, such as simple groups. In particular, the projective special linear groups over small fields provide a rich vein of interesting cases on which to hang the general theory.

Organiser: Prof. Leonard Soicher
Details: Level |Semester A|15 credits
Subject area: Pure mathematics
Overlaps:

None

Essential prerequisites:
• MTH5100 Algebraic Structures I
• See module organiser before registering.

MTH6104 Algebraic Structures II

Restrictions:

None

Assessment:

#### Normal assessment

DescriptionDuration / LengthWeighting
Final examination 3 hours 100%

#### Associate assessment

DescriptionDuration / LengthWeighting
Final examination 3 hours 100%

#### Reassessment

DescriptionDuration / LengthWeighting
Resit examination 3 hours 100%
Syllabus:
1. Revision of basic group theory, isomorphism theorems, Jordan-Holder theorem, Sylow's theorems, the structure theorem for finite abelian groups.
2. Permutation groups: transitivity, primitivity, symmetric and alternating groups. Maximal subgroups, wreath products, Iwasawa's Lemma. The outer automorphism of S6.
3. Linear groups: finite fields, general linear groups, projective special linear groups. Projective lines and isomorphisms of some projective special linear groups with alternating groups. Simplicity of PSLn(q).
Learning outcomes:

This module covers:

• A review of undergraduate group theory.
• Permutation group theory.
• Matrix groups.
• Simple groups.

#### Disciplinary Skills

At the end of this module, students should be able to:

• State the main definitions and theorems covered in this module.
• Prove certain results covered in this module and its exercises.
• Calculate in various types of groups, such as dihedral groups, permutation groups, and matrix groups.
• Demonstrate the capacity for abstract, mathematical, precise thinking.

#### Attributes

At the end of this module, students should have developed with respect to the following attributes:

• Acquire and apply knowledge in a rigorous way.
• Apply their analytical skills to investigate unfamiliar problems.
• Acquire substantial bodies of new knowledge.
• Explain and argue clearly and concisely.
• Connect information and ideas within their field of study.

#### Assessment Criteria

History:

Approved by Faculty Board for MSc 05/96. Approved for MSci 05/03.