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In this note, it is proved the existence of an infinitely generatedmultiplicative group consisting of entire functions that are, except for theconstant function 1, hypercyclic with respect to the convolution operatorassociated to a given entire function of subexponential type. A certainstability under multiplication is also shown for compositional hypercyclicityon complex domains.

Multiplicative structures of hypercyclic functions for convolution operators