I have questions about structure of groups.
Is there bijection between Cayley tables and (finite) groups?
So, Cayley table is a table of permutations of finite elements in which none element repeat in any row and any column. And, so, every group has to satisfy this and thus can be represented as Cayley table.
Edit: I meant bijection between general Cayley table $n$ by $n$ (order of rows and colums doesn't matter) and group with $n$ elements. In on other words, if you give me $m$ by $m$ Cayley table is there unique group with $m$ elements? (Reverse holds because of group properties.)