Bijections generating the near-ring of zero-preserving functions on a finite group
by
Christian Neumaier
Department of Algebra, Johannes Kepler Universität Linz

Let <G, + > be a (not necessarily abelian) finite group. The set M₀(G):={f:G --> G | f(0)=0} of all zero-preserving functions on G together with the operation + of pointwise addition forms a group. Furthermore, M₀(G) is closed under composition of functions o . We will show that a randomly chosen bijection b in M₀(G) generates (with respect to the operations +, o ) the set M₀(G) with probability nearly one.

Date received: May 17, 2004