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

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_۱} \oplus \cdots \oplus \mathbb{Z}_{d_t} , on a set of \(m\) elements, and several illustrative examples are presented to clarify the main results.

کلیدواژه ها:

Orbit-stabilizer ، Finitely generated Abelian group ، Group actions