KenÕs Group Theory Notes

(Spring 2007)

Last updated at 6:20 PM, April 25, 2007

 

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Recent Announcements     

              

Recent Assignments

 

Brief notes

Weeks 1-3 (Jan 8, 10, 22, 22, 24, 24), Groups and homomorphisms, the isomorphism theorems (chapters 1 & 2.)

           Assignment 1 (.pdf)

           Assignment 2 (.pdf)

           Assignment 3 (.pdf)

           Assignment 4 (.pdf)

 

Weeks 4-6 (Jan 29, 31, Feb 5, 12, 14, 21), Group action (chapter 3)

           Please note the two .pdf files in these notes.  One contains the subgroup lattice of S4; the other is a list of all the 3-colorings of the 2x2 square.  This second pdf file is needed for Wednesday, January 31.

           Assignment 5 (.pdf)

           Take-home Midterm.  (Due at noon on Friday, March 2.)

           Solution to Quizzes 2 & 3 (.pdf)

           Solution to Quiz 4 (.pdf)

           Solution to Quiz 5 (.pdf)

           Sample problems for the midterm (.pdf)

 

March 14 -- Midterm Exam.

 

Weeks 8-10 (March 19, 21, 26, 28, April 2, 2), The Sylow theorems and their applications (chapter 4). 

           Assignment 6 (.pdf)

           Assignment 7 (.pdf)

           Assignment 8 (.pdf)

           Solution to Quiz 6 (.pdf)

           Solution to Quiz 7 (.pdf)

           Solution to Quiz 8 (.pdf)

           Solution to Quiz 9 (.pdf)

 

Weeks 11-13 (April 4, 4, 9, 11, 16, 18),  Group extensions (chapters 5, 6, 7)

           Normal series (parts of chapter 5)

           Finite Direct Products (parts of chapter 6),

           Notes on semidirect products.  Extensions and semi-direct products (parts of chapter 7),

           Assignment 9 (.pdf)

           Solution to Quiz 10 (.pdf)

 

Weeks 14-15, Linear groups (parts of chapter 8)

 

Wed, April 25, 6:30-8:30  Review for Final Exam.

 

Monday, April 30, 5-8:30 PM – Final Exam.

 

Some interesting web links

           Math Forum Notes on Group Theory.

           WikipediaÕs introduction to group theory.

           History of the group concept.

           The dihedral group in color.

           Groups of order 16 or less and groups of order 400 or less.

                       (Type  >NumberSmallGroups(n); at the GAP prompt to get the number of groups of order n, for n < 2^11.)

           Tilings of the plane and Islamic art and wallpaper groups.  David JoyceÕs webpage on wallpaper groups.

           Three dimensional space groups and crystallography.

           MSC (Mathematical Subject Classification) #20.

           KenÕs electronic library on group theory.

 

Course Documents

Textbook: Joseph T. Rotman, An Introduction to the Theory of Groups, Fourth Edition, Springer-Verlag, 1995. (ISBN 0-387-94285-8)

 

GAP:  We will use GAP software for computations in group theory.  This software is freely available for download and easy to install on most computers.  (There are several Macs in the Mac lab that also have GAP installed.)  I recommend that you go to the GAP webpage and follow the instructions there to install GAP on your computer.

           There is an abstract algebra GAP manual by Rainbolt and Gallian available online.

 

Here is the course syllabus (.pdf) or the same syllabus in Microsoft Word.

 

Review materials

You might wish to review your Modern Algebra textbook (such as the one by Gallian.)

 

Old Announcements

           (none)

 

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