Abstract:This paper is motivated by a recent one of Stewart and Towers  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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- © 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