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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A product variety of groups with distributive lattice
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by L. F. Harris PDF
Proc. Amer. Math. Soc. 43 (1974), 53-56 Request permission

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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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 43 (1974), 53-56
  • MSC: Primary 20E10
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0332986-2
  • MathSciNet review: 0332986