# Checker for Baby Monster group B
# SJN 19/8/2004

# Check orders from definition.
chor 1 2
chor 2 3
mu 1 2 3       # ab
chor 3 55
mu 3 2 4     
mu 3 4 5     
mu 3 5 6     
mu 6 3 7     
mu 7 4 8     
mu 3 8 9     
mu 9 4 10      # ababababbababbabb
chor 10 23

# Show that a is a 2C element.
mu 5 9 11    
mu 5 11 12     # ababbababbababababbababb
chor 12 52
pwr 26 12 13   # c: a 2C element
mu 1 13 14     # ac
chor 14 35     # ac has order 35, so a is in 2C.

# We now need to show that b is in 3A rather than 3B.
# A product 2A*3B can never have order 2, 4, 8 or 14, but the
# product 2A*3A can.
mu 9 10 15
chor 15 38
pwr 19 15 16   # d: a 2A element
cj 2 1 17
mu 16 17 18
chor 18 8      # db^a has order 8, so b must be in 3A.