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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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Frattini subalgebras of finitely generated soluble Lie algebras
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by Ralph K. Amayo PDF
Trans. Amer. Math. Soc. 236 (1978), 297-306 Request permission

Abstract:

This paper is motivated by a recent one of Stewart and Towers [8] investigating Lie algebras with “good Frattini structure” (definition below). One consequence of our investigations is to prove that any finitely generated metanilpotent Lie algebra has good Frattini structure, thereby answering a question of Stewart and Towers and providing a complete Lie theoretic analogue of the corresponding group theoretic result of Phillip Hall. It will also be shown that in prime characteristic, finitely generated nilpotent-by-finite-dimensional Lie algebras have good Frattini structure.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 236 (1978), 297-306
  • MSC: Primary 17B30; Secondary 17B65
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0498733-7
  • MathSciNet review: 0498733