Theorems on Cartan subalgebras like some on Carter subgroups
HTML articles powered by AMS MathViewer
- by Ernest L. Stitzinger PDF
- Trans. Amer. Math. Soc. 159 (1971), 307-315 Request permission
Abstract:
We consider some results on the Cartan subalgebras of a solvable Lie algebra which are analogues to some results on Carter subgroups of a finite solvable group. Only solvable Lie algebras are considered here.References
- Donald W. Barnes, Nilpotency of Lie algebras, Math. Z. 79 (1962), 237β238. MR 150177, DOI 10.1007/BF01193118
- Donald W. Barnes, On Cartan subalgebras of Lie algebras, Math. Z. 101 (1967), 350β355. MR 220785, DOI 10.1007/BF01109800
- S. Bauman, A note on cover and avoidance properties in solvable groups, Proc. Amer. Math. Soc. 21 (1969), 173β174. MR 238950, DOI 10.1090/S0002-9939-1969-0238950-4
- R. W. Carter, On a class of finite soluble groups, Proc. London Math. Soc. (3) 9 (1959), 623β640. MR 114859, DOI 10.1112/plms/s3-9.4.623
- Roger W. Carter, Nilpotent self-normalizing subgroups of soluble groups, Math. Z. 75 (1960/61), 136β139. MR 123603, DOI 10.1007/BF01211016
- R. W. Carter, Nilpotent self-normalizing subgroups and system normalizers, Proc. London Math. Soc. (3) 12 (1962), 535β563. MR 140570, DOI 10.1112/plms/s3-12.1.535
- Roger Carter and Trevor Hawkes, The ${\cal F}$-normalizers of a finite soluble group, J. Algebra 5 (1967), 175β202. MR 206089, DOI 10.1016/0021-8693(67)90034-8 P. Hall, On the system normalizers of a soluble group, Proc. London Math. Soc. 43 (1937), 507-528.
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703, DOI 10.1007/978-3-642-64981-3
- G. B. Seligman, Modular Lie algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 40, Springer-Verlag New York, Inc., New York, 1967. MR 0245627, DOI 10.1007/978-3-642-94985-2
- R. W. Carter, Splitting properties of soluble groups, J. London Math. Soc. 36 (1961), 89β94. MR 133368, DOI 10.1112/jlms/s1-36.1.89
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 159 (1971), 307-315
- MSC: Primary 17.30
- DOI: https://doi.org/10.1090/S0002-9947-1971-0280556-9
- MathSciNet review: 0280556