Fajan, russel, soddy in 1913 gives the group displacement law which states that on the emission of alpha particle the new element lies two columns left in periodic table and mass no. decreased by 4 units and on the emission of beta particle the new element lies  one column right in periodic table and mass no. remains the same
If you were referring to the Soddy's group displacement law with respect to nuclear derives out of his generalization of alpha and beta matter 

Soddy's first generalization came in his rule that loss of an alpha particle from an atom with an even number in the periodic table produces an atom with the next lower even number. In subsequent changes, however, when alpha emission does not take place, a reversion to the original "family" may occur, and the products will be chemically inseparable from the starting material, even though the atomic weights vary. Complementary to this alpha-particle rule is the one that in beta emissions an atom moves up one place in the periodic table. 

In 1913 Soddy combined the alpha and beta rules into the group displacement law: one alpha emission causes a shift two places back in the periodic table, and one beta emission causes a shift one place further on. Hence a sequence of alpha-beta-beta emissions would mean a return to the original place in the table.