Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Theorems on Cartan subalgebras like some on Carter subgroups


Author: Ernest L. Stitzinger
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] D. Barnes, Nilpotency of Lie algebras, Math. Z. 79 (1962), 237-238. MR 27 #180. MR 0150177 (27:180)
  • [2] -, On Cartan subalgebras of Lie algebras, Math. Z. 101 (1967), 350-355. MR 36 #3837. MR 0220785 (36:3837)
  • [3] S. Bauman, A note on cover and avoidance properties in solvable groups, Proc. Amer. Math. Soc. 21 (1969), 173-174. MR 0238950 (39:310)
  • [4] R. Carter, On a class of finite soluble groups, Proc. London Math. Soc. (3) 9 (1959), 623-640. MR 22 #5677. MR 0114859 (22:5677)
  • [5] -, Nilpotent self-normalizing subgroups of soluble groups, Math. Z. 75 (1960/61), 136-139. MR 23 #A928. MR 0123603 (23:A928)
  • [6] -, Nilpotent self-normalizing subgroups and system normalizers, Proc. London Math. Soc. (3) 12 (1962), 535-563. MR 25 #3988. MR 0140570 (25:3988)
  • [7] R. Carter and T. Hawkes, The $ F$-normalizers of a finite soluble group, J. Algebra 5 (1967), 175-202. MR 34 #5914. MR 0206089 (34:5914)
  • [8] P. Hall, On the system normalizers of a soluble group, Proc. London Math. Soc. 43 (1937), 507-528.
  • [9] B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin and New York, 1967. MR 37 #302. MR 0224703 (37:302)
  • [10] G. Seligman, Modular Lie algebras, Springer-Verlag, Berlin and New York, 1967. MR 39 #6933. MR 0245627 (39:6933)
  • [11] R. Carter, Splitting properties of soluble groups, J. London Math. Soc. 36 (1961), 89-94. MR 24 #A3202. MR 0133368 (24:A3202)

Similar Articles

Retrieve articles in Transactions 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/S0002-9947-1971-0280556-9
Keywords: Cartan subalgebra
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society