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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A product variety of groups with distributive lattice


Author: L. F. Harris
Journal: Proc. Amer. Math. Soc. 43 (1974), 53-56
MSC: Primary 20E10
MathSciNet review: 0332986
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Abstract: By a variety of $ A$-groups is meant a locally finite variety of groups whose nilpotent groups are abelian. It is shown that if $ \mathfrak{U}$ is a variety of $ A$-groups and $ \mathfrak{B}$ is a locally finite variety whose lattice of subvarieties is distributive and the exponents of $ \mathfrak{U}$ and $ \mathfrak{B}$ are coprime, then the lattice of subvarieties of the product variety $ \mathfrak{U}\mathfrak{B}$ is distributive.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0332986-2
Article copyright: © Copyright 1974 American Mathematical Society