Frattini subalgebras of finitely generated soluble Lie algebras
HTML articles powered by AMS MathViewer
- by Ralph K. Amayo
- Trans. Amer. Math. Soc. 236 (1978), 297-306
- DOI: https://doi.org/10.1090/S0002-9947-1978-0498733-7
- PDF | 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.References
- Ralph K. Amayo, Engel Lie rings with chain conditions, Pacific J. Math. 54 (1974), 1–12. MR 360727
- Ralph K. Amayo and Ian Stewart, Finitely generated Lie algebras, J. London Math. Soc. (2) 5 (1972), 697–703. MR 323850, DOI 10.1112/jlms/s2-5.4.697 —, Infinite-dimensional Lie algebras, Noordhoff, Groningen, 1974.
- Donald W. Barnes and Martin L. Newell, Some theorems on saturated homomorphs of soluble Lie algebras, Math. Z. 115 (1970), 179–187. MR 266969, DOI 10.1007/BF01109856
- Charles W. Curtis, Noncommutative extensions of Hilbert rings, Proc. Amer. Math. Soc. 4 (1953), 945–955. MR 59254, DOI 10.1090/S0002-9939-1953-0059254-7
- Nathan Divinsky, Rings and radicals, Mathematical Expositions, No. 14, University of Toronto Press, Toronto, Ont., 1965. MR 0197489
- Jacques Dixmier, Algèbres enveloppantes, Cahiers Scientifiques, Fasc. XXXVII, Gauthier-Villars Éditeur, Paris-Brussels-Montreal, Que., 1974 (French). MR 0498737
- David Towers and Ian Stewart, The Frattini subalgebras of certain infinite-dimensional soluble Lie algebras, J. London Math. Soc. (2) 11 (1975), no. 2, 207–215. MR 396710, DOI 10.1112/jlms/s2-11.2.207
Bibliographic 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