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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Frattini subalgebras of finitely generated soluble Lie algebras


Author: Ralph K. Amayo
Journal: Trans. Amer. Math. Soc. 236 (1978), 297-306
MSC: Primary 17B30; Secondary 17B65
MathSciNet review: 0498733
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0498733-7
PII: S 0002-9947(1978)0498733-7
Keywords: Lie algebra, Frattini subalgebra
Article copyright: © Copyright 1978 American Mathematical Society