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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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.
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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