Module Details |
| The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module. |
| Title | GROUP THEORY | ||
| Code | MATH343 | ||
| Coordinator |
Prof AV Pukhlikov Mathematical Sciences Pukh@liverpool.ac.uk |
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| Year | CATS Level | Semester | CATS Value |
| Session 2016-17 | Level 6 FHEQ | First Semester | 15 |
Aims |
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To introduce the basic techniques of finite group theory with the objective of explaining the ideas needed to solve classification results. |
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Learning Outcomes |
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Understanding of abstract algebraic systems (groups) by concrete, explicit realisations (permutations, matrices, Mobius transformations). |
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The ability to understand and explain classification results to users of group theory. |
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The understanding of connections of the subject with other areas of Mathematics. |
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To have a general understanding of the origins and history of the subject. |
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Syllabus |
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| 1 |
Definitions and examples. Cyclic, dyhedral and symmetric groups. Abelian groups. Orders of elements. Subgroups, cosets and Lagrange''s Theorem. Normal subgroups and quotient groups. Automorphisms. Semi-direct products. The Homomorphism Theorem. The Orbit-Stabiliser Theorem. Mobius transformations. The Sylow Theory. Applications of Sylow Theory to classification problems. |
Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. Explanation of Reading List: J.Humphreys. A course in Group Theory. (Any edition.) |
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Pre-requisites before taking this module (other modules and/or general educational/academic requirements): |
| MATH101; MATH103; MATH142*; MATH244*; MATH247* *Either MATH142, MATH244 or MATH247 required. **MATH142 is an alternative prerequisite for MATH342. |
Co-requisite modules: |
Modules for which this module is a pre-requisite: |
| MATH342**; MATH449; MATH442** |
Programme(s) (including Year of Study) to which this module is available on a required basis: |
Programme(s) (including Year of Study) to which this module is available on an optional basis: |
| Programme:G100 Year:3 Programme:G101 Year:3,4 Programme:G110 Year:3 Programme:G1F7 Year:3 Programme:G1N2 Year:3 Programme:G1R9 Year:4 Programme:GG13 Year:3 Programme:GN11 Year:3 Programme:GG14 Year:3 Programme:GL11 Year:3 Programme:BCG0 Year:3 Programme:GR11 Year:3 Programme:GV15 Year:3 Programme:L000 Year:3 Programme:MMAS Year:1 |
Assessment |
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| EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
| Unseen Written Exam | 2.5 hours | First semester | 90 | Yes | Standard UoL penalty applies | Assessment 2 Notes (applying to all assessments) Assessment 1 is a class test. Assessment 2 is a written exam. The rubric: Candidates may attempt all questions. Best FIVE answers will be taken into account. Each question carries the same weight. |
| CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
| Coursework | 80 minutes class tes | First semester | 10 | No reassessment opportunity | University policy. | Assessment 1 There is no reassessment opportunity, class test is not reassessed |