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Transactions of the American Mathematical Society

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

 
 

 

Critical groups having central monoliths of a nilpotent by abelian product variety of groups


Author: James J. Woeppel
Journal: Trans. Amer. Math. Soc. 225 (1977), 155-161
MSC: Primary 20E10
DOI: https://doi.org/10.1090/S0002-9947-1977-0424942-8
MathSciNet review: 0424942
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Abstract: Let $\mathfrak {N}$ be a variety of groups which has nilpotency class two and finite odd exponent. Let $\mathfrak {A}$ be an abelian variety of groups with finite exponent relatively prime to the exponent of $\mathfrak {N}$. The existence in the product variety $\mathfrak {N}\mathfrak {A}$ of nonnilpotent critical groups having central monoliths is established. The structure of these critical groups is studied. This structure is shown to depend on an invariant, k. The join-irreducible subvariety of $\mathfrak {N}\mathfrak {A}$ generated by the nonnilpotent critical groups of $\mathfrak {N}\mathfrak {A}$ having central monoliths is determined, in particular, for k odd.


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Keywords: Varieties of groups, join-irreducible varieties, Cross varieties, critical group, central monolith, nilpotent by abelian
Article copyright: © Copyright 1977 American Mathematical Society