Join-irreducible cross product varieties of groups
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- by James J. Woeppel PDF
- Trans. Amer. Math. Soc. 200 (1974), 141-148 Request permission
Abstract:
Let $\mathfrak {U},\mathfrak {B}$ be varieties of groups which have finite coprime exponents, let $\mathfrak {U}$ be metabelian and nilpotent with βsmallβ nilpotency class, and let $\mathfrak {B}$ be abelian. The product variety $\mathfrak {U}\mathfrak {B}$ is shown to be join-irreducible if and only if $\mathfrak {U}$ is join-irreducible. This is done by obtaining a simple description for the critical groups generating $\mathfrak {U}\mathfrak {B}$ when $\mathfrak {U}$ is join-irreducible and finding a word which is not a law in $\mathfrak {U}\mathfrak {B}$ but is a law in every proper subvariety of $\mathfrak {U}\mathfrak {B}$References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 200 (1974), 141-148
- MSC: Primary 20E10
- DOI: https://doi.org/10.1090/S0002-9947-1974-0364451-5
- MathSciNet review: 0364451