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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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0424942-8
Keywords: Varieties of groups, join-irreducible varieties, Cross varieties, critical group, central monolith, nilpotent by abelian
Article copyright: © Copyright 1977 American Mathematical Society

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