Let G be a finite group, and consider the multiplication tablefor G, i.e., the t

Question

Let G be a finite group, and consider the multiplication tablefor G, i.e., the table that gives the binary operation of G---                          Columns             *    a       b       c      d             a |   a      c       b     d                |    R      b |     c      a       d      b    O        |    W     c |    b      d        a      c   S         |             d|      d      b        c      a Show that every element of G occurs precisely once in each rowof the table and precisely once in each column. Let G be a finite group, and consider the multiplication tablefor G, i.e., the table that gives the binary operation of G---                          Columns             *    a       b       c      d             a |   a      c       b     d                |    R      b |     c      a       d      b    O        |    W     c |    b      d        a      c   S         |             d|      d      b        c      a Show that every element of G occurs precisely once in each rowof the table and precisely once in each column.

Explanation / Answer

Given set {a,b,c,d} with respect to the binary operatioon * , as given by the table, do not form a group as there is no identity element.So given property of composition table can't be proved.

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