Minimal nonnilpotent solvable Lie algebras

Author:
Ernest L. Stitzinger

Journal:
Proc. Amer. Math. Soc. **28** (1971), 47-49

MSC:
Primary 17.30

MathSciNet review:
0271178

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We shall say that a solvable Lie algebra is a minimal nonnilpotent Lie algebra if is nonnilpotent but all proper subalgebras of are nilpotent. It is shown here that if is a minimal nonnilpotent Lie algebra, then is the vector space direct sum of and where is an ideal in is a one-dimensional subalgebra of , either is a minimal ideal of or the center of coincides with the derived algebra, , of and in either case acts irreducibly on .

**[1]**Donald W. Barnes,*Nilpotency of Lie algebras*, Math. Z.**79**(1962), 237–238. MR**0150177****[2]**Donald W. Barnes and Humphrey M. Gastineau-Hills,*On the theory of soluble Lie algebras*, Math. Z.**106**(1968), 343–354. MR**0232807****[3]**N. Bourbaki, Livre XXVI:*Groupes et algébres de Lie*. Chap. 1, Actualités Sci. Indust., no. 1285, Hermann, Paris, 1960. MR**24**#A2641.**[4]**P. Hall,*On system normalizers of a soluble group*, Proc. London Math. Soc. (2)**43**(1937), 507-528.**[5]**P. Hall and Graham Higman,*On the 𝑝-length of 𝑝-soluble groups and reduction theorems for Burnside’s problem*, Proc. London Math. Soc. (3)**6**(1956), 1–42. MR**0072872**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
17.30

Retrieve articles in all journals with MSC: 17.30

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0271178-X

Keywords:
Fitting decomposition,
Engel's Theorem

Article copyright:
© Copyright 1971
American Mathematical Society