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Groups and FieldsMediumGroups and the Group Axioms

Groups and the Group Axioms · Medium problem

Two tables are proposed as the Cayley table of some 44-element group with identity ee. Table PP: row 11 is e,a,b,ce,a,b,c; row 22 is a,e,c,ba,e,c,b; row 33 is b,c,e,ab,c,e,a; row 44 is c,b,a,ac,b,a,a. Table QQ: row 11 is e,a,b,ce,a,b,c; row 22 is a,b,c,ea,b,c,e; row 33 is b,c,e,ab,c,e,a; row 44 is c,e,a,bc,e,a,b. One of the two tables cannot be the Cayley table of ANY group, because some row repeats a symbol instead of containing each of e,a,b,ce,a,b,c exactly once. In that bad row, how many times does the most-repeated symbol appear?