Let be an operation on a finite set G. Form the operation table. Prove that if .G; / is
Chapter 40, Problem 40.15(choose chapter or problem)
Let be an operation on a finite set G. Form the operation table. Prove that if .G; / is a group, then in every row and in every column, each element of G appears exactly once. Show that the converse of this assertion is false; that is, construct an operation on a finite set G such that in every row and in every column, each element of G appears exactly once, but .G; / is not a group. 40.1
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