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).