
Professor Gordana G. Todorov 

MTH 3175 · Group Theory 
Fall 2013 
Course Description
The course presents basic concepts and techniques of the group theory: symmetry groups, axiomatic definition of groups, important classes of groups (abelian, cyclic, additive and multiplicative groups of residues, permutation groups), Cayley table, subgroups, group homomorphisms, cosets, the Lagrange theorem, normal subgroups, quotient groups, direct products. Studies structural properties of groups. Possible applications include geometry, number theory, crystallography, physics, and combinatorics.
Grading Policies
There will be 5 quizzes. You will be allowed to drop your lowest quiz grade. If you miss a quizz for justifyable reason (illness or any other serious problem), you may drop one more quiz grade. There will be no make up quizzes.
Quizzes count 60% and Final exam is 40%
Course letter grades require the following minimum percent grades: A (95%), A(90%), B+(86.7%), B(83.4%), B(80%), C+(76.7%), C(73.4%), C(70%), D+(66.7%), D(63.4%), D(60%)
Course Policies
1. Students are responsible for ALL information and announcements given when they are absent.
2. If you must leave class early, please, see me before class. No other early departures or walking during the class will be tolerated, with the exception of severe medical problems.
3. All cellphones must be turned off! If you are expecting important phone call, please, see me before class. Points will be deducted each time you use your phone in class!
4. It is University policy that no grade, including an incomplete, can be changed after one year. Exceptions must be authorized by the Academic Standing Committee.
5. All students without legitimate conflicts (approved by the instructor) will take the final exam at the scheduled time. Do not make travel plans that conflict with the final exam.
About the course and you!
This is a very beautiful course, with a lot of theory together with, both examples and strict proofs.
You will be expected to write proper mathematical proofs!
You are expected to do a lot of work in this course!
You are expected to do HW without my collecting it and checking up on you. Discussion of the HW will form the first part of the next class.
PLEASE REMEMBER, YOUR SUCCESS DEPENDS ON YOUR WORK!!!
W, Sep 4  Ch.0  Preliminaries  HW p21: 1,2,4,7,8,9,11,14,20,21,22,53,54 
Th, Sep 5  Ch.0  Preliminaries 
M, Sep 9  Ch.1  Examples of symmetry groups  HW p35: 5,13,17,19,20,22 
W, Sep 11  Ch.2  Definition and Examples of Groups  HW p52: 1, 2, 3, 4, 5, 6, 7, 8 
Th, Sep 12  Ch.2  Elementary properties of groups  HW p52: 9, 14, 15, 16, 20, 23, 25, 32, 34 
M, Sep 16  Ch.3  Finite Groups; Subgroups  HW p64: 1, 2, 3, 10, 12, 18, 19, 20, 23, 26, 30 
W, Sep 18  Ch.3  Finite Groups; Subgroups  HW p67: 36, 37, 38, 39, 46, 47, 48, 51, 59, 60 
Th, Sep 19  Quiz 1 & Solving some additional problems from Ch.3 
M, Sep 23  Ch.4  Properties of Cyclic Groups  HW p81: 110, 14, 21, 26, 28 
W, Sep 25  Ch.4  Classification of Sugroups of Cyclic Groups  HW p83: 36,37,38,39,46,47,48,49, 50,51,59,60, 65, 66, 67 
Th, Sep 26  Ch.4  Cyclic Groups & Supplementary Exercises p91: 110, 17, 18, 22, 23,24,26, 27, 34, 35, 36 
M, Sep 30  Ch.5 Permutations  HW p113: 1, 2, 3, 4, 5, 6, 7, 8, 9, 17, 18, 23, 24, 25, 26, 
W, Oct 2  Ch.5 Permutations  HW p113: 27, 28, 31, 33, 43, 55, 58, 59 
Th, Oct 3  Quiz 2 & additional problems from Ch.5 
M, Oct 7  Ch.6  Isomorphisms  HW p133: 110, 14, 24, 25, 27, 29, 31, 32, 35, 37, 39 
W, Oct 9  Ch.6  Isomorphisms  HW p133: 35, 37, 39, 40, 47 
Th, Oct 10  Ch.6  Cosets and Lagrange's Theorem  HW p149: 19, 13, 14, 15, 16, 18, 25, 26 
M, Oct 14  Ch.7  ............................. Columbus Day  No NU classes .......................... 
W, Oct 16  Ch.7  Cosets and Lagrange's Theorem  HW p150: 34, 35, 38, 39, 45, 46, 47, 48, 50 
Th, Oct 17  Quiz 3 & Ch.8  External Direct Product  HW p174: 120, 22, 24, 26, 27 
M, Oct 21  Ch.8  External Direct Product  HW p169: 44, 45,46,49, 53, 59, 62, 63, 74, 75 
W, Oct 23  Ch.8 & Supplementary Exercises p174: 5, 6, 7, 10, 13, 14, 25, 26,35, 50 
Th, Oct 24  Ch.9  Normal Subgroups  HW 193: 1,2,3,4,5,7,13,15,16,17,19,21 
M, Oct 28  Ch.9  Normal Subgroups 
W, Oct 30  Ch.9  Factor Groups  p193: 10,14,15,16,17,18 
Th, Oct 31  Quiz 4 & Ch.9  Factor Groups  p193: 27,28,29,30,32,33,34,37,38,40,45,46,49,50,51,53,54,65,66,68 
M, Nov 4  Ch.10  Group homomorphisms, The First Isomorphism Theorem  p211: 527,48,53,54,55,56,62 
W, Nov 6  Ch.11  Fundamental Theorem of Finite Abelian Groups  p230: 1,3,4,5,7,13,15,16,17,19,21 
Th, Nov 7  Ch.11  Isomorphism Classes of Abelian Groups 
M, Nov 11  ..................................... Veteran's day  no classes ..................... 
W, Nov 20  Group Actions 
Th, Nov 21  Quiz 5 & Group Actions 
M, Nov 25  Ch. 24  Syllow Theorems  p.414: 58, 1014, 1622 
W, Nov 27  ................................... Thanksgiving recess ..................................... 
Th, Nov 28  ................................... Thanksgiving day ......................................... 
M, Dec 2  Ch.24  Syllow Theorems  p. 414: 2428,30,31,39,40, 46,47 & Applications of Syllow Theorems 
W, Dec 4  Review  Last day of NU classes 
Th, Dec 5  ................................... Reading Day ................. No NU classes .......... 

Started: September 11, 2009 
Last modified: September 3, 2013 

