This paper investigates the automorphism group of monogenic  semigroups (or monoids) to find its relationship with the automorphism group of cyclic groups. Then, by considering a presentation related to the direct product of monogenic semigroups, verify the relationship between the automorphism group of These and the automorphism group of the group presented by the same presentation. This study gives us some explicit formulas for computing the order of automorphism groups of these algebraic structures.
Automorphism groups of algebraic structures, Monogenic  semigroups and monoids
AHMADIDELIR, KARIM and DOOSTIE, HOSSEIN
"On the automorphisms of direct product of monogenic semigroups and monoids,"
Turkish Journal of Mathematics: Vol. 36:
1, Article 8.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss1/8