# Checker for Co_3

# Check orders from definition
chor 1 3
chor 2 4
mu 1 2 3
chor 3 14

# b^2 is in 2A, so if o(ab^2) = 24, then a must be in 3A or 3C.
mu 3 2 4
chor 4 24

# Find elements commuting with b^2
mu 2 2 5
cj 5 4 6
mu 5 6 7
pwr 3 7 8         # This element is in C(b^2)
mu 3 4 9
mu 9 2 10
mu 10 1 11
mu 11 1 12
cj 5 12 13
mu 5 13 14
mu 14 14 15
mu 12 15 16       # This element is in C(b^2)

# Write a word in these elements which has order 5 and which commutes
# with b. Because 5 does not divide the order of C(4B), we know
# b is a 4A element.
mu 8 16 17
mu 17 16 18
pwr 3 18 19
pwr 6 17 20
mu 19 20 21
chor 21 5         # Check order
com 21 2 22
chor 22 1         # Check it commutes with b

# It remains to show that a is not in 3C (we used fingerprinting
# for this).

# 22/09/04 - it turns out that these relations are redundant!
#chor 4 24
#mu 4 2 23
#chor 23 10
#chor 9 14

