Generalized factorizable automorphisms in n-component conjoint structures

Abstract

The group of generalized factorizable automorphisms (Math. Soc. Sci. 36 (1998) 91) of a n-component conjoint structure, which satisfies certain solvability assumptions and the Thomsen condition, is proved to be the semidirect product of its normal subgroup of factorizable automorphisms and a subgroup isomorphic to the symmetric group of degree n. This sets the frame for discussing how solvability assumptions are mirrored by properties of automorphisms, for deriving results on the existence of factorizable automorphisms, and for relating the generalized factorizable automorphisms to the isomorphisms of the concatenation structures induced on the components of a conjoint structure. It is concluded that the generalized factorizable automorphisms do not provide any contribution to the independence of factors of a n-component conjoint structure other than that already captured by the group of factorizable automorphisms. The results do not draw upon Archimedean axioms.