a a b b b b a a a b Figure 1: The Cayley graph of the symmetries of the tetrahedron a) What is the order of the element ab? b) Do a and c commute and how can you C tell? What about a and b? c) Starting at your choice of e, how many vertices total can you reach using only edges band c? (This set of vertices represents the subgroup generated by b and c. Let's call it H.)
a a b b b b a a a b Figure 1: The Cayley graph of the symmetries of the tetrahedron a) What is the order of the element ab? b) Do a and c commute and how can you C tell? What about a and b? c) Starting at your choice of e, how many vertices total can you reach using only edges band c? (This set of vertices represents the subgroup generated by b and c. Let's call it H.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
6
![a
a
b.
b
b
b
b
a
a
a
a
b
b
Figure 1: The Cayley graph of the symmetries of the tetrahedron
a) What is the order of the element ab?
b) Do a and c commute and how can you
tell? What about a and b?
c) Starting at your choice of e, how many
vertices total can you reach using only
edges band c? (This set of vertices
represents the subgroup generated by b
and c. Let's call it H.)
C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff228f7fd-3407-42e7-ac94-596cf803a70b%2F34e5698f-30bf-4d8e-adf0-0c739f632b30%2F5swqc6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a
a
b.
b
b
b
b
a
a
a
a
b
b
Figure 1: The Cayley graph of the symmetries of the tetrahedron
a) What is the order of the element ab?
b) Do a and c commute and how can you
tell? What about a and b?
c) Starting at your choice of e, how many
vertices total can you reach using only
edges band c? (This set of vertices
represents the subgroup generated by b
and c. Let's call it H.)
C.
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