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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Boolean powers: direct decomposition and isomorphism types


Authors: Kenneth Hickin and J. M. Plotkin
Journal: Trans. Amer. Math. Soc. 265 (1981), 607-621
MSC: Primary 08A99; Secondary 06E99, 20E15
DOI: https://doi.org/10.1090/S0002-9947-1981-0610969-0
MathSciNet review: 610969
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Abstract: We determine properties of Boolean powers of groups and other algebraic structures, and we generalize Jónsson's theorem on Boolean powers of centerless, directly indecomposable groups. We show that every nonabelian, finitely generated group has $ {2^{{\aleph _0}}}$ nonisomorphic countable Boolean, and hence subcartesian, powers. We show that nonabelian groups $ G$ such that either (i) $ G$ is not the central product of two nonabelian groups or (ii) every pair of nontrivial normal subgroups of $ G$ intersect nontrivially yield nonisomorphic Boolean powers with respect to nonisomorphic Boolean algebras.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0610969-0
Article copyright: © Copyright 1981 American Mathematical Society