Geodesic
Automorphism Groups of Unary Algebras on Groups
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1165-1171

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This paper presents a systematic study of the automorphism groups of those unary (universal) algebras whose carrier set G is the carrier set of some group ) and whose automorphism set contains the right translations of the latter group. These algebras appear, apart from the known classical contexts, repeatedly in characterization theorems of endomorphism semigroups (End) and automorphism groups (Aut) of algebras due to Grätzer (3; 4; 5), Makkai (7), Armbrust and Schmidt (1), Birkhoff (2), and others.Our main result (Theorem 1) constitutes an essential strengthening of a theorem of Birkhoff and represents the automorphism group of a unary algebra (where F is contained in the set of left translations of the group as wreath product of two groups that are easily determined from F and G. 
Wenzel, G. H. Automorphism Groups of Unary Algebras on Groups. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1165-1171. doi: 10.4153/CJM-1969-127-2
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