MATH 446/546. SECOND TEST. SOLUTIONS.
When proving statements, you are allowed to use homework problems and facts
from the book or from the lectures.
Good luck!
Problem 1. (25 points) Let G be a nite
MATH 446/546. SECOND PRACTICE TEST. SOLUTIONS.
Problem 1. The quaternion group is a group of order 8, G = cfw_1, i, j, k ,
with dening relations
i = jk = kj,
j = ki = ik,
k = ij = ji,
i2 = j 2 = k 2 =
MATH 446/546. SECOND TEST.
When proving statements, you are allowed to use homework problems and facts
from the book or from the lectures.
Good luck!
Problem 1. (25 points) Let G be a nite group, V a
MATH 446/546. SECOND PRACTICE TEST
Problem 1. The quaternion group is a group of order 8, G = cfw_1, i, j, k ,
with dening relations
i = jk = kj,
j = ki = ik,
k = ij = ji,
i2 = j 2 = k 2 = 1.
a) Find
MATH 446/546. FIRST HOURLY TEST. SOLUTIONS.
Problem 1. Let G be a group of order 5 7 19. Prove that G is cyclic.
Solution. We have from Sylows theorem that n5 = n7 = n19 = 1. Thus, G has
normal subgro
MATH 256. SECOND MIDTERM.
All problems are worth 25 points, but some are harder then the others. When
proving statements, you are allowed to use homework problems and facts from the
book or from the l
Math 446/546. First Hourly Test. Problems from
past exams.
Problem 1. Prove that any group of order 105 is solvable.
Solution. Let np (p = 3, 5, 7) be the number of Sylow p-subgroups of G. It
follows
MATH 256. FIRST MIDTERM.
All problems are worth 25 points, but some are harder then the others. When
proving statements, you are allowed to use homework problems and facts from the
book or from the le
.
MATH 446/546. PRACTICE FINAL
Problem 1. Let F be the splitting eld of the polynomial x3 + 2x 1 = 0 over
Z3 .
a) What is the degree of F over Z3 ?
b) What is the Galois group of F over Z3 ?
Solution.
.
MATH 446/546. PRACTICE FINAL
Problem 1. Let F be the splitting eld of the polynomial x3 + 2x 1 = 0 over
Z3 .
a) What is the degree of F over Z3 ?
b) What is the Galois group of F over Z3 ?
Problem 2