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 au…
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