Algebra B 1 - 0366-2132-03
Spring Semester, 2012/13
Mikhail Borovoi ( borovoi@post.tau.ac.il )
Tuesday 17-18
Wednesday 14-16
Exercises: Yotam Smilansky (yotamsky@yahoo.com),
Ran Azouri (ransass@tau.ac.il)
Tuesday 16-17
Procedural Matters:
Prerequisite Courses: Linear Algebra 1, Linear Algebra 2 in parallel.
Course syllabus:
Permutations. Groups, homomorphisms.
Quotient spaces, Theorem of Lagrange.
Normal subgroups, quotient groups. Cyclic groups.
Isomorphism theorems.
Action of a group on a set, orbits. Theorem of Cayley.
p-groups, Sylow subgroups, Theorems of Sylow.
Finitely generated abelian groups.
The simplicity of the alternating group An.
Solvable groups.
Textbook:
An Introduction to the Theory of Groups, 4th Edition (or any other edition),
by Joseph J. Rotman.
Exam:
On the exam in 2013 the students should answer 4 questions from 5.
One or two of the questions will be to prove a theorem
(or a proposition, or a lemma) from the course.
Example of exam
Lectures in Hebrew on the Internet:
Alexander Lubotzky, Algebraic structures
Moshe Jarden, Algebra B 1
Mikhail Borovoi, Algebra B 1. Handwritten course notes from Spring 2010
Useful Internet resource: Mathematics - Stack Exchange
Contact me at: borovoi@post.tau.ac.il.
Please write in Subject: Algebra B 1 (in English).