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Course: MATH 3106, Fall 2009School: ECCD
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FOR PROBLEMS TUTORIAL 5 AND ASSIGNMENT 5. Problem 1. Find the commutator subgroup Q of the quaternion group Q. Problem 2. (2) Find all (3) Find all (4) Find all (1) Compute the order |g| for all g D4 . conjugacy classes in D4 . normal subgroups of D4 . homomorphic images of D4 . Problem 3. Draw the lattice diagram for G if G (1) = S3 . (2) G = D4 . Defend your answer! Problem 4. Show that D4 is not isomorphic...
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FOR PROBLEMS TUTORIAL 5 AND ASSIGNMENT 5.
Problem 1. Find the commutator subgroup Q of the quaternion group Q. Problem 2. (2) Find all (3) Find all (4) Find all (1) Compute the order |g| for all g D4 . conjugacy classes in D4 . normal subgroups of D4 . homomorphic images of D4 .
Problem 3. Draw the lattice diagram for G if G (1) = S3 . (2) G = D4 . Defend your answer! Problem 4. Show that D4 is not isomorphic to Q. Problem 5. Show that C /C0 R+ , where R+ denotes the = group of positive real numbers under multiplic...
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ECCD - MATH - 3106
INTRODUCTION TO GROUP THEORY MATH 3106, FALL 2006Tutorial 1, Sep 18 Example 1. Show that if p > 2 is a prime number and a = 0(mod p), then the equation x2 a2(mod p) has exactly two solutions in Z. p Example 2. Un = {z1, z2, . . . , zn} C is a cyc
ECCD - MATH - 3106
INTRODUCTION TO GROUP THEORY MATH 3106, FALL 2006Tutorial 2, Sep 25 Example 1. Prove that Sn =< (12), (13), . . . , (1n) >, n 3. Example 2. Prove that the two cycles (1352) and (2461) are conjugate in S8. Example 3. Prove that the two permutations
ECCD - MATH - 3106
INTRODUCTION TO GROUP THEORY MATH 3106, FALL 2006Tutorial 3, Oct 2 Claim 1. Let G be a group and g G be an element of G. Recall that CG(g) = {a G | ag = ga} is the centralizer of g in G. Then xgx-1 = ygy -1 x-1y CG(g). Claim 2. Let X be a gener
ECCD - MATH - 3106
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ECCD - MATH - 3106
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ECCD - MATH - 3106
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ECCD - MATH - 3106
INTRODUCTION TO GROUP THEORY MATH 3106, FALL 2006Assignment 3Due date: Monday, October 2 at 13:30.Problem 1. Generators for Sn and for An . Let n 3. (1) Prove that Sn =< (12), (123 . . . n) >. (2) Prove that An =< (123), (124), . . . , (12n) >.
ECCD - MATH - 3106
INTRODUCTION TO GROUP THEORY MATH 3106, FALL 2006Assignment 4Due date: Monday, October 16 at 13:30.Problem 1. Find a subgroup of S4 isomorphic to the group (a) Z3 ; (b) K4 . Problem 2. Show that GL2 (R) is not isomorphic to the multiplicative gr
ECCD - MATH - 3106
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ECCD - MATH - 3106
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ECCD - MATH - 3106
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