Professor Alexandru I. Suciu MATH 3175 · Group Theory Fall 2010

## Course Information

 Course MATH 3175 · Group Theory: Sec. 1, CRN 14982 and Sec. 2, CRN 15767 Instructor Alex Suciu Course Web Site www.math.neu.edu/~suciu/MATH3175/ugroup.fa10.html Time and Place Section 1:  Mon, Wed, Th 10:30am-11:35am, in 247 Ryder Hall Section 2:  Mon, Wed, Th 9:15am-10:20am, in 427 Ryder Hall Office 441 LA – Lake Hall Phone (617) 373-4456 Email a.suciu@neu.edu Office Hours Mon, Wed 4:30-5:30pm in 441LA, or by appointment Teaching Assistant Yinbang Lin.  Email: lin.yinb@husky.neu.edu Phone: x-7055. Office hours:  Tue 10:00-11:00am, in 551NI, or by appointment. Prerequisites: MATH 2331 Linear Algebra Textbook Contemporary Abstract Algebra, 7th Edition, by Joseph A. Gallian, Brooks/Cole, 2010. ISBN: 0547165099 Course Description The course introduces some of the basic ideas and applications of group theory. We will study various classes of group (such as symmetry groups, abelian, cyclic, and permutation groups), and also subgroups, normal subgroups, cosets, the Lagrange theorem, group homomorphisms, quotient groups, direct products, group actions on a set, and the Sylow theorems. The theory will be illustrated by examples from geometry, linear algebra, number theory, crystallography, and combinatorics. Further topics will be covered as time permits. Grade Based on quizzes (40%), midterm exam (20%), and final exam (40%).

## Class Materials

### Homework assignments

Chapter Topic Pages Problems
0 Preliminaries 21–24 1, 2, 4, 7, 8, 9, 11, 14, 20, 21, 22, 53, 54
2 Definition and Examples of Groups 52 1, 2, 3, 4, 5, 6, 7, 8
Elementary Properties of Groups 52–54 9, 14, 15, 16, 20, 23, 25, 32, 34
3 Finite Groups; Subgroups 64–67 1, 2, 3, 10, 12, 18, 19, 20, 23, 26, 30
Finite Groups; Subgroups 67–69 36, 37, 38, 39, 46, 47, 48, 51, 59, 60
4 Properties of Cyclic Groups 81–83 1–10, 14, 21, 26, 28
Classification of Sugroups of Cyclic Groups 83–85 36, 37, 38, 39, 46, 47, 48, 51, 59, 60
Cyclic Groups & Supplementary Exercises 91–93 1, 2, 3, 9, 18, 22, 23, 34
5 Permutation Groups 113–115 1–9, 17, 18, 23, 24, 25
Permutation Groups 115–117 27, 28, 31, 33, 43, 58, 59
6 Isomorphisms 133–135 1–10, 14, 24, 25
Isomorphisms 135 27, 28, 29, 31, 35, 39, 40
7 Cosets and Lagrange's Theorem 149–150 1–9, 13, 14, 16, 18, 25, 26
Cosets and Lagrange's Theorem 150–152 27, 34, 35, 38, 39, 45, 46, 49
8 External Direct Products 167–170 1–13, 16 18, 20, 22, 24, 26, 27, 44, 45, 53, 59, 63
Supplementary Exercises 174–176 5, 10, 13, 14, 25, 26, 35
11 Fundamental Theorem of Finite Abelian Groups 226–228 1, 3, 4, 5, 7, 13, 15, 17, 19, 21
9 Normal Subgroups 193 1, 2, 3, 4, 5, 6, 8
Factor Groups 193–194 10, 14, 16, 17, 18, 27, 28, 29, 30, 32, 34,
Factor Groups 195–197 37, 38, 40, 45, 46, 49, 50, 51, 53, 54, 65, 66, 68
10 Homomorphisms, Kernels, and Images 211–213 5, 7–27, 54, 55, 62

### Quizzes

 Department of Mathematics Office: 441 Lake Hall Messages: (617) 373-2450 Northeastern University Phone: (617) 373-4456 Fax: (617) 373-5658 Boston, MA, 02115 Email: a.suciu@neu.edu Directions