Math 103A Fall 2006 Exam 1
NAME: Answers
Problem 1 /30
Problem 2 /20
Problem 3 /30
Problem 4 /20
Total /100
1
Problem 1 (30 points)
1 Let D4 = cfw_R0 , R90 , R180 , R270 , S1 , S2 , S3 , S4 be the dihedral group of order
8, which consists of symmetries o
MATH 103A
Exam 1
January 30, 2013
INSTRUCTIONS READ THIS NOW
This test has 5 problems on 1 page worth a total of 50 points.
Write your name and PID on the cover of your Blue Book right now.
Write your solutions clearly in your Blue Book. Carefully indi
Math 103A Fall 2007 Exam 1
October 31, 2007
NAME:
Problem 1 /30
Problem 2 /25
Problem 3 /25
Problem 4 /20
Total /100
1
Problem 1 (30 points)
1 Let D3 = cfw_R0 , R120 , R240 , S1 , S2 , S3 be the dihedral group of order 6,
which consists of symmetries of
Math 103A Fall 2007 Exam 1
October 31, 2007
NAME: Solutions
Problem 1 /30
Problem 2 /25
Problem 3 /25
Problem 4 /20
Total /100
1
Problem 1 (30 points)
1 Let D3 = cfw_R0 , R120 , R240 , S1 , S2 , S3 be the dihedral group of order 6,
which consists of symm
Math 103A Fall 2006 Exam 1
w/solutions
NAME: Anne Sirs
Problem 1 /30
Problem 2 /20
Problem 3 /30
Problem 4 /20
Total /100
1
Problem 1 (30 points)
1 Let D4 = cfw_R0 , R90 , R180 , R270 , S1 , S2 , S3 , S4 be the dihedral group of order
8, which consists o
Math 103A Fall 2005 Exam 2
November 9, 2005
NAME:
Problem 1 /30
Problem 2 /20
Problem 3 /15
Problem 4 /20
Problem 5 /15
Total
1
Problem 1 (30 points)
1a (10 pts) List all of the subgroups of the cyclic group Z27 .
1b (10 pts) How many elements of order 3
MATH 103A Practice Problems for the Final
Alina Bucur
2. Write down 5 dierent groups of order 24, such that no two of them are isomorphic to each other.
Prove that no two are isomorphic.
Solution. Z8 Z3 , Z4 Z2 Z3 , Z2 Z2 Z2 Z3 , D12 , S4 .
The rst three
Math 103A Fall 2005 Final
December 9, 2005
Show all work. Problems whose answers are a single number or yes or no may
not get credit if there is no explanation for the answer. You may quote without proof any theorems or results we stated in class or that
MATH 103A Practice Problems for the Final
Alina Bucur
Please do not make any assumptions about the composition of the exam from this set of review problems.
Do not assume that the exam questions will be exactly as the questions below, or slight modication
MATH 103A
Exam 2
February 22, 2013
INSTRUCTIONS READ THIS NOW
This test has 5 problems on 1 page worth a total of 50 points.
Write your name and PID on the cover of your Blue Book right now.
Write your solutions clearly in your Blue Book. Carefully ind
Math 103A Fall 2007 Exam 2
November 19, 2007
NAME:
Problem 1 /25
Problem 2 /25
Problem 3 /20
Problem 4 /30
Total /100
1
Problem 1 (25 points)
(a) (5 pts). Clearly state Lagranges theorem.
2
(b) (20 pts) Let p be a prime number. Let G be a group with |G| =