# Checker for Thompson group Th

# Check orders from the definition
chor 1 2
chor 2 3
mu 1 2 3
chor 3 19

# It suffices to show that b is in class 3A.
# Construct another 3A element by powering up an element of order 21
mu 3 2 4
mu 3 4 5
mu 3 3 6
mu 6 5 7
chor 7 21
pwr 7 7 8

# Construct a 3A element whose product with b has order 2.
mu 3 5 9
pwr 4 4 10
mu 4 6 11
mu 11 9 12
mu 12 4 13
mu 13 9 14
mu 14 10 15
mu 15 6 16
mu 16 3 17
cj 8 17 18    # This is another 3A element
mu 2 18 19
chor 19 2     # Product has order 2 with b, so b is a 3A element.