HW3_322_F09

HW3_322_F09 - Fall 2009 MAT 322: ALGEBRA WITH GALOIS THEORY...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fall 2009 MAT 322: ALGEBRA WITH GALOIS THEORY PROBLEM SET #3 Week #1: October 5th - October 11th. Topics : Linear independence of characters, fixed point lemma, conjugacy classes, centralizers, centers, p-groups are supersolvable, groups of order 2 p are cyclic or dihedral, groups of order p 2 are abelian, permutations groups, cycles, A n is simple for n ≥ 5, Sylow p-subgroups, Sylow’s three theorems. Read : GT [58-62] and GT [68-75] Problems due Friday, October 9th, at 4:00 pm in Martin Luu’s mailbox: • Problem 1 : Show that Q / Z is isomorphic to μ ∞ ( C ) , the group of z ∈ C * such that z n = 1 for some positive integer n . Is it a finitely generated abelian group? What is the torsion subgroup of Q / Z ? • Problem 2 : Let G be a group, and let G der be the subgroup generated by all commutators [ x,y ] = xyx- 1 y- 1 , for x,y ∈ G . Show that G der is a normal subgroup of G , and that the corresponding quotient group G ab is abelian....
View Full Document

This note was uploaded on 05/07/2010 for the course MAT 322 at Princeton.

Page1 / 2

HW3_322_F09 - Fall 2009 MAT 322: ALGEBRA WITH GALOIS THEORY...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online