Counting actions and non-isomorphic actions of a finitely generated abelian group on a finite set

Document Type : Research Articles

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Department of Mathematics Education, Farhangian University, P. O. Box 14665–889, Tehran, Iran

Abstract

The main goal of the paper is to compute the number of group actions and actions up to isomorphism of a finitely generated Abelian group $ G \cong \mathbb{Z}^k \oplus \mathbb{Z}_{d_1} \oplus \cdots \oplus \mathbb{Z}_{d_t} $, on a set of \(m\) elements, and several illustrative examples are presented to clarify the main results.

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