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Given Group(Non-abelian) Multiplication Table.
Find $ca,bb\text{ and }df$.

$\begin{array}{ l | c r r r r r } * & e & a & b & c & d &f \\ \hline e & e & a & b & c & d & f \\ a & a & b & e & d \\ b&b\\ c&c&&&e&&a\\ d&d\\ f&f\\ \end{array}$


My question:

Is there an algorithm for filling up the empty cells? if there isnt, what is then the best approach?

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    Hint: Each row and each column must contain each of $a,b,c,d,e,f$ exactly once.2012-11-18

1 Answers 1

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There may not be enough information to fill in the whole table, but there’s enough to answer the question. For instance, $ca=c(cf)=(cc)f=ef=f$. Note that $bb=(aa)b$ and $df=(ac)f$; can you take it from there?

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    @JL90: I didn’t check every single entry, but I checked enough to be pretty sure that it is, yes.2012-11-18