Vol. 98, No. 2, 1982

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Zero-inducing functions on finite abelian groups

George Lucius O’Brien

Vol. 98 (1982), No. 2, 381–391

Let G be a finite abelian group and let f : G G be any function. Let rx : G G be the function rx(y) = x + y, x G. A study is made of conditions on f such that the semi-group of functions generated by f and all rx under composition contains the zero function. If G is cyclic, it is necessary and sufficient that f not be one-to-one. In general some necessary conditions are given and a partial converse is given for these conditions, which involve the behaviour of f on subgroups and cosets of G.

Mathematical Subject Classification 2000
Primary: 20K01
Secondary: 05C99, 68A05
Received: 30 July 1980
Published: 1 February 1982
George Lucius O’Brien