Isomorphism universal varieties of Heyting algebras

Authors:
M. E. Adams, V. Koubek and J. Sichler

Journal:
Trans. Amer. Math. Soc. **319** (1990), 309-328

MSC:
Primary 06D20; Secondary 03G25, 08A35, 18B15

DOI:
https://doi.org/10.1090/S0002-9947-1990-0955486-9

MathSciNet review:
955486

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Abstract: A variety is *group universal* if every group is isomorphic to the automorphism group of an algebra ; if, in addition, all finite groups are thus representable by finite algebras from , the variety is said to be *finitely group universal*. We show that finitely group universal varieties of Heyting algebras are exactly the varieties which are not generated by chains, and that a chain-generated variety is group universal just when it contains a four-element chain. Furthermore, we show that a variety of Heyting algebras is group universal whenever the cyclic group of order three occurs as the automorphism group of some . The results are sharp in the sense that, for every group universal variety and for every group , there is a proper class of pairwise nonisomorphic Heyting algebras for which .

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DOI:
https://doi.org/10.1090/S0002-9947-1990-0955486-9

Article copyright:
© Copyright 1990
American Mathematical Society