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Transactions of the American Mathematical Society

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

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Critical groups having central monoliths of a nilpotent by abelian product variety of groups
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by James J. Woeppel PDF
Trans. Amer. Math. Soc. 225 (1977), 155-161 Request permission

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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Additional Information
  • © Copyright 1977 American Mathematical Society
  • 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