‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعــــة سلمان بن عبد العزيز‬
‫كليـة العلوم والدراسات اإلنسانية‬
‫باألفالج‬
‫قسم الرياضيات طالبات‬
Kingdom of Saudi Arabia
Ministry of Higher Education
Salman bin Abdul Aziz University
College of Arts and Science
Al-Aflaj
Mathematics Department
‫التوصيف المختصر المسلم للطالبات‬
‫في بداية الفصل الدراسي االول‬
‫هـ‬1435-1434
‫ ريض‬3440 :‫الرمز والرقم‬
‫ نظرية الزمر‬:‫أسم المقرر‬
)3،1،0(3 :‫الوحدات الدراسية‬
‫ الخامس‬:‫المستوي‬
‫ ريض‬2250 :‫متطلب سابق‬
:‫محتويات المقرر‬
Course Code: MAT 3440
Course Title: Group Theory
Credit Hours: 3(3,1,0)
Level: Fifth
Prerequisites: MAT 2250
‫ نظرية‬- ‫ التشاكل الزمري‬-‫ زمر التماثل‬- ‫ الزمرة الدائرية – زمر التباديل‬- ‫ الزمرة الجزئية‬- ‫ الخواص األساسية للزمرة‬- ‫تعريف الزمرة‬
‫ الزمر المتماثلة‬- ‫ زمر الدوران المنتهية‬- ‫ الصيغ الثنائية‬- ‫ الزمر المنتهية‬- ‫ زمرة القسمة‬- ‫ المجموعات المصاحبة ونظرية الجرانج‬- ‫كيلي‬
‫ نظرية‬- P ‫ زمرة‬- ‫ الزمر الهرمتية‬- ‫ الزمر المولدة‬- ‫ الزمر اآلبلية منتهية التوليد‬- ‫ الزمر اآلبلية‬- ‫ نظرية الطيف‬- ‫ الزمر الناظمية‬‫ الزمر‬-‫ الزمر القابلة للحل‬- ‫ تركيب المتسلسالت‬- ‫ المتسلسالت الناظمية‬- ‫ نتيجة شاير‬- ‫ الزمر البسيطة‬-‫ نظريات سيلو‬- ‫التشاكل الزمري‬
.‫المتالشية‬
Course Description:
Fundamental properties of Groups Subgroups – Cyclic Groups – Permutation Groups – Symmetry Groups –
Group Homeomorphisms and Cayley Theorem – Cosets and Lagrange's Theorem – Quotient Groups – Finite
Groups – Discrete Groups – Finite Rotation Groups – Normal and Factor Groups – Bilinear Forms – Symmetric
Forms – Hermitian Forms – The Spectral Theorem – The Rotation Group – Abelian Groups – Finitely Generated
Abelian Groups – P– Group - The Isomorphism Theorems of Groups – Sylow Theorems – Simple Group –
Group Representation – Schur's Lemma – Normal and Subnormal Series – Composition Series – Soluble Groups
– Nilpotent Groups.
Knowledge
1. Understand and know the scientific background of Groups, Subgroups, Cyclic Groups, Permutation
Groups, Symmetry Groups.
2. Understand the theories and principles of Group Homeomorphisms and Cayley Theorem.
3. Understand the relationships between Cosets and Lagrange's Theorem, Quotient Groups.
4. Have a scientific background about the nature of Finite Groups.
5. Demonstrate knowledge & different approaches for Normal subgroups and Factor Groups.
6. Acquire scientific idea of Bilinear Forms, Symmetric Forms, Hermitian Forms, The Spectral Theorem.
7. Understand and know the scientific background of Abelian Groups, Finitely Generated Abelian Groups.
8. Demonstrate knowledge & different approaches for P– Group, The Isomorphism Theorems of Groups,
Sylow Theorems.
9. Have a scientific background about the nature of Simple Group – Group Representation.
10. Understand the theories and principles of Schur's Lemma, Normal and Subnormal Series, Composition
Series.
11. Know the processes and methods of Soluble Groups, Nilpotent Groups.
1
‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعــــة سلمان بن عبد العزيز‬
‫كليـة العلوم والدراسات اإلنسانية‬
‫باألفالج‬
‫قسم الرياضيات طالبات‬
Kingdom of Saudi Arabia
Ministry of Higher Education
Salman bin Abdul Aziz University
College of Arts and Science
Al-Aflaj
Mathematics Department
Cognitive Skills
1. To define and recognize the basic concepts of Groups, homeomorphisms , cosets,
normal subgroups, p-groups, simple groups, normal series, nilpotent groups.
2. To derive the basic properties of all concepts in 1.
3. To construct factor groups, homeomorphisms, normal series.
4. To classify all finite abelian groups of a specified order.
5. To be able to prove elementary theorems involving concepts mentioned in 1.
6. To be able to find out Co-sets and Quotient Groups.
7. To be able to give counter examples to show that the converse of some implications is
not necessarily true.
8. To be able to use Sylows theorems in deriving conclusions about finite groups.
9. To be able to state and prove famous theorem in group theory such as Sylow’s
theorems, Lagrange Theorem, Cauchy theorem,… etc.
1 Topics to be Covered
Topic
Fundamental properties of groups and examples
No of Contacth
Weeks ours
2
8
Subgroups
1
4
Cyclic groups, Permutation groups, Symmetry Groups
1
4
Group homeomorphisms and Cayley theorem
1
4
Cosets and Lagrange theorem
1
4
Quotient Groups & Finite groups
1
4
Normal subgroups and factor group
1
4
Finitely generated abelian groups
1
4
p-groups Isomorphism theorems and Sylow theorems
1
4
Simple groups and group representation
1
4
Schur’s lemma
1
4
Normal and Subnormal Series and Composition Series
1
4
Soluble Groups and Nilpotent Groups
1
4
Total
14
56
2
‫المملكة العربية السعودية‬
‫وزارة التعليم العالي‬
‫جامعــــة سلمان بن عبد العزيز‬
‫كليـة العلوم والدراسات اإلنسانية‬
‫باألفالج‬
‫قسم الرياضيات طالبات‬
Kingdom of Saudi Arabia
Ministry of Higher Education
Salman bin Abdul Aziz University
College of Arts and Science
Al-Aflaj
Mathematics Department
5. Schedule of Assessment Tasks for Students During the Semester
Assess
Assessment task
1
Week due
Proportion of Final Assess
Performance
All along
10%
Pop Quizzes & web tests
All along
5%
3
First exam
Week 7
4
Second exam
5
Final examination
2
Week 12
Week 16
10%
10%
60%
1. Required Text(s)
Artin M., "Algebra", Englewood Cliffs, NJ: Prentice- Hall, ISBN: 013004763.
2. Essential References
J. Gallian, Contemporary Abstract Algebra, seventh edition, Brooks Cole, 2009.
Attendance.
1) The class attendance is mandatory and the students have to attend a minimum
of 75% of class sessions in the course.
2) No excused absences are permitted. An absence for any reason (including late
registration) counts and a grade Denied (DN) will be shown in his transcript.
3) Absence will be considered from the first week.
4) You are not allowed to attend any class if you did come ten minutes after the
beginning time of the class. ( i.e. if the class begins at 10:00 am, then any student
comes at 10:11 pm is not allowed to attend the class and will be considered as
absent).
3