# Black box algorithm to find standard generators of McL.2 set F 0 # Have we found element 1? set G 0 # Have we found element 2? set V 0 # Timeout counter for "semi-standard" part set Y 0 # Timeout counter for conjugating part lbl SEMISTD rand 1 ord 1 A incr V if V gt 1000 then timeout if A notin 1 2 3 4 5 6 7 8 9 10 11 12 14 15 20 22 24 30 then fail if F eq 0 then if A eq 22 then pwr 11 1 2 set F 1 endif endif if G eq 0 then if A eq 6 then pwr 2 1 3 set G 1 # This is likely to be an element in class 3B # (probability 30/31). endif endif if F eq 0 then jmp SEMISTD if G eq 0 then jmp SEMISTD set X 0 set Z 0 lbl CONJUGATE incr Y if Y gt 1000 then timeout rand 4 cjr 3 4 mu 2 3 5 ord 5 D if D notin 2 4 6 8 10 12 20 22 24 then # This is not McL.2! fail endif if D in 4 22 24 then # The second element is definitely in class 3B. set Z 1 endif if Z eq 0 then incr X if X gt 10 then # We have haven't been able to prove that the # second element is in class 3B. # We guess that it probably isn't, and start # looking again. set G 0 jmp SEMISTD endif endif if D noteq 22 then jmp CONJUGATE mu 5 3 6 # abb mu 5 6 7 # ababb mu 5 5 8 # abab mu 8 7 9 mu 9 7 10 mu 10 6 11 ord 11 E if E noteq 24 then jmp CONJUGATE lbl FINISH oup 2 2 3