Section 1: TR 12:30-1:45 OldH 203
Instructor: Dr. Hermiller
Office: 304 Avery Hall, 472-7238             Email: smh at math dot unl dot edu
Course web page: Link: http://www.math.unl.edu/~ smh/911/
Office hours: T 11:00-12:15, R 1:45-3:00

Corequisite: Math 817 and Math 872, or consent of instructor. (Math 872 may be taken concurrently, or may not be needed - I'll eventually assume some familiarity with finitely presented groups and fundamental groups. If you want to review some of this material, you may find the Math 872 text helpful: Algebraic Topology by Allen Hatcher, available electronically at the author's web site, http://www.math.cornell.edu/~hatcher/AT/ATpage.html.)

Course description: This course will be an introduction to the theory of groups, with an emphasis on infinite groups. Several methods for studying groups, including topological, algebraic, and geometric techniques, will be discussed in this course. We'll begin in the first two weeks with a large catalog of groups that group theorists often to study, mostly because of their applicability in topology and geometry; we'll use these as examples for all of the rest of the course. We'll also talk about some basics of group theory, including decomposing groups (as semidirect products, HNN extensions, etc.), picturing groups with Cayley complexes, and the virtually/residually/locally/relatively properties of groups. After that, we will spend the bulk of the semester focusing on an introduction to two more specific areas of group theory. The first will be ``poly properties'' of groups, including nilpotence and solvability. Poly properties can be used to measure how close a group is to being abelian, free, or just about any other property of groups. Often theorems that hold for groups with a property P can be shown by induction also to hold for a group that is poly-P. The second main topic will be geometric group theory, and in particular growth functions and series, connections to dynamical systems, and/or measuring complexity of algorithms for groups.

Text: There will be no formal text for the course, but much of the material we will cover in the first topic of the course can be found in the book A Course in the Theory of Groups by D.J.S. Robinson (Springer, 1996), and some material for the second part of the course can be found in Topics in Geometric Group Theory by P. de la Harpe (U. Chicago Press, 2000).

Requirements: Each two or three weeks I will be assigning some homework problems. These will vary in difficulty from easy to the size of a small project (expect a few of this size). Depending on the nature of the problems, I will either ask you to hand in written solutions, or else I will expect you to present or discuss the material in class. Late homework won't be accepted except in extreme circumstances. You may work on the homework in groups if you wish, although I recommend that you each try the problems and proofs individually before talking them over with other people. When it is written, the homework must be written up individually, even if the problems are solved by a group of students - several identical copies of the same solutions will not be accepted. The grade for the course will be based completely on the homework.

Notes: I'd like to encourage you to ask questions during lectures. At the beginning of each class, if you have a question on the material we've covered so far, or if you're thoroughly stuck on a homework problem, please feel free to ask about it. If I say something confusing during the class, also please let me know. I very much prefer lectures to be interactive.

Miscellaneous legal stuff: Students who believe their academic evaluation has been prejudiced or capricious have recourse for appeals to (in order) the instructor, the departmental chair, the departmental appeals committee, and the college appeals committee. Friday, January 20 is the last day to drop a course and not have it appear on your transcript. Friday, March 2 is the last day to change a course registration to or from ``Pass/No Pass''. Friday, April 6 is the last day to drop a course with a grade of W (withdrawal).

S. Hermiller