# 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