Conjugacy theorems for a class of locally finite Lie algebras

 Access to full text

 Full (PDF)

1. [1] R.K. Amayo and Ian Stewart: Infinite-dimensional Lie algebras. Noordhoff International, Leyden1974. Zbl0302.17006MR396708
2. [2] R.K. Amayo and Ian Stewart: Descending chain conditions for Lie algebras of prime characteristic. J. Algebra (to appear). Zbl0311.17006MR374218
3. [3] D.W. Barnes and H.M. Gastineau-Hills: On the theory of soluble Lie algebras. Math. Z.106 (1968) 343-354. Zbl0164.03701MR232807
4. [4] D.W. Barnes and M.L. Newell: Some theorems on saturated homomorphs of soluble Lie algebras. Math. Z.115 (1970) 179-187. Zbl0197.03003MR266969
5. [5] A. Borel: Linear algebraic groups. Ann. of Math. (2) 64 (1956) 20-82. Zbl0070.26104MR204532
6. [6] A. Borel: Linear algebraic groups. Benjamin, New York1969. Zbl0186.33201MR251042
7. [7] N. Bourbaki: Topologie Générale I. 3rd edition, Hermann, Paris1961. Zbl0249.54001
8. [8] N. Bourbaki: General Topology part 1. Addison-Wesley, Reading Massachusetts1966. Zbl0301.54001
9. [9] R.W. Carter: Nilpotent self-normalizing subgroups of soluble groups. Math. Z.75 (1961) 136-139. Zbl0168.27301MR123603
10. [10] C. Chevalley: Théorie des groupes de Lie, tome II: groupes algébriques. Hermann, Paris1951. Zbl0054.01303MR51242
11. [11] P. Deligne: Private communication, 1973. 
12. [12] A.D. Gardiner, B. Hartley and M.J. Tomkinson: Saturated formations and Sylow structure in locally finite groups. J. Algebra17 (1971) 177-211. Zbl0215.10605MR272897
13. [13] W. Gaschütz: Zur Theorie der endlichen auflösbaren Gruppen. Math. Z.80 (1963) 300-305. Zbl0111.24402MR179257
14. [14] A. Grothendieck: Éléments de Géometrie algébrique IV(1). Publ. Math. I.H.E.S.20 (1964) 101-355. Zbl0136.15901
15. [15] B. Hartley: Locally nilpotent ideals of a Lie algebra. Proc. Cambridge Philos. Soc.63 (1967) 257-272. Zbl0147.28201MR213402
16. [16] J.E. Humphreys: Introduction to Lie algebras and representation theory, Graduate texts in mathematics 9. Springer, Berlin1972. Zbl0254.17004MR499562
17. [17] N. Jacobson: Lie algebras, Interscience. New York1962. Zbl0121.27504MR143793
18. [18] A.A. Klimowicz: Fitting and formation theory in locally finite groups, Ph.D. thesis. University of Warwick1973. Zbl0304.20020
19. [19] A.A. Klimowicz: Formation theory in locally finite groups (to appear). Zbl0304.20020MR384936
20. [20] A.A. Klimowicz: Sylow structure and basis normalizers in a class of locally finite groups (to appear). Zbl0356.20033MR396757
21. [21] A.G. Kuroš: Theory of groups vol. 2, translated by K.A. Hirsch.Chelsea, New York1956. MR80089
22. [22] J.-P. Serre: Groupes proalgébriques. Publ. Math. I.H.E.S. 7 (1960) 341-403. Zbl0097.35901MR118722
23. [23] L.A. Simonjan: Two radicals of Lie algebras. Dokl. Akad. Nauk. SSSR157 (1964) 281-283; Soviet Math. Doklady5 (1964) 941-944. Zbl0136.30403MR163936
24. [24] I.N. Stewart: The minimal condition for subideals of Lie algebras. Math. Z.111 (1969) 301-310. Zbl0179.33203MR251093
25. [25] I.N. Stewart: An algebraic treatment of Mal'cev's theorems concerning nilpotent Lie groups and their Lie algebras. Compositio Math.22 (1970) 289-312. Zbl0204.35903MR288158
26. [26] I.N. Stewart: Structure theorems for a class of locally finite Lie algebras. Proc. London Math. Soc (3) 24 (1972) 79-100. Zbl0225.17005MR289592
27. [27] I.N. Stewart: Levi factors of infinite-dimensional Lie algebras. J. London Math. Soc. (2) 5 (1972) 488. Zbl0249.17013MR323851
28. [28] I.N. Stewart : Author-abstract of [26]. Zbl. 225 (1972) 109. Zbl0225.17005
29. [29] I.N. Stewart: Chevalley-Jordan decomposition for a class of locally finite Lie algebras (to appear). Zbl0351.17013
30. [30] I.N. Stewart: Cartan subalgebras of certain locally finite Lie algebras (to appear). 
31. [31] I.N. Stewart: The Wedderburn-Mal'cev theorems in a locally finite setting (to appear). Zbl0326.16020
32. [32] E.L. Stitzinger: Theorems on Cartan subalgebras like some on Carter subgroups. Trans. Amer. Math. Soc.159 (1971) 307-315. Zbl0238.17009MR280556
33. [33] S.E. Stonehewer: Abnormal subgroups of a class of periodic locally soluble groups. Proc. London Math. Soc. (3) 14 (1964) 520-536. Zbl0123.24902MR165012
34. [34] S.E. Stonehewer: Locally soluble FC-groups. Arch. der Math.16 (1965) 158-177. Zbl0135.04803MR179263
35. [35] S.E. Stonehewer: Formations and a class of locally soluble groups. Proc. Cambridge Philos. Soc.62 (1966) 613-635. Zbl0145.02503MR204529
36. [36] M.J. Tomkinson: Formations of locally soluble FC-groups. Proc. London Math. Soc. (3) 19 (1969) 675-708. Zbl0179.32302MR260881
37. [37] D.A. Towers: A Frattini theory for algebras. Proc. London Math. Soc. (3) 27 (1973) 440-462. Zbl0267.17004MR427393
38. [38] W. Tuck: Frattini theory for Lie algebras. Ph.D. thesis, University of Sydney1969. 
39. [39] B.A.F. Wehrfritz: Soluble periodic linear groups. Proc. London Math. Soc. (3) 18 (1968) 141-157. Zbl0157.06002MR220842
40. [40] D.J. Winter: Abstract Lie algebras. M.I.T. Press, Cambridge Massachusetts1972. Zbl0248.17003MR332905

1. Ian Stewart, Chevalley-Jordan decomposition for a class of locally finite Lie algebras