Question: how to join or meet for words of permutation group

for example

a*b v a^-1 = b

i guess Disj or Conj are Max or Min respectively

however i do not know how to max(a,b) where a and b are permutation group

reference from L group in


if can not calculate this, do not know how to determine whether equal in a*b v a^-1 = b

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