Minimal non-elementary Lie algebras
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- by Kristen Stagg and Ernest Stitzinger PDF
- Proc. Amer. Math. Soc. 139 (2011), 2435-2437 Request permission
Abstract:
Minimal non-elementarty finite groups must be nilpotent. The Lie algebra analogue admits non-nilpotent examples. We classify them for complex solvable Lie algebras.References
- Donald W. Barnes, On Cartan subalgebras of Lie algebras, Math. Z. 101 (1967), 350โ355. MR 220785, DOI 10.1007/BF01109800
- Camelia Ciobanu, On a class of Lie $p$-algebras, Acta Math. Acad. Paedagog. Nyhรกzi. (N.S.) 24 (2008), no.ย 3, 279โ285. MR 2469949
- Camelia Ciobanu, Some results on E-$p$-algebras, Proc. Rom. Acad. Ser. A Math. Phys. Tech. Sci. Inf. Sci. 10 (2009), no.ย 3, 5. MR 2539804
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- Joseph Kirtland, Finite groups with a minimal Frattini subgroup property, Glasg. Math. J. 45 (2003), no.ย 1, 41โ44. MR 1972691, DOI 10.1017/S0017089502008960
- Mark Lincoln and David Towers, The Frattini $p$-subalgebra of a solvable Lie $p$-algebra, Proc. Edinburgh Math. Soc. (2) 40 (1997), no.ย 1, 31โ40. MR 1437809, DOI 10.1017/S0013091500023415
- Ernest L. Stitzinger, Frattini subalgebras of a class of solvable Lie algebras, Pacific J. Math. 34 (1970), 177โ182. MR 274540
- Ernest L. Stitzinger, Theorems on Cartan subalgebras like some on Carter subgroups, Trans. Amer. Math. Soc. 159 (1971), 307โ315. MR 280556, DOI 10.1090/S0002-9947-1971-0280556-9
- D. A. Towers, Elementary Lie algebras, J. London Math. Soc. (2) 7 (1973), 295โ302. MR 376782, DOI 10.1112/jlms/s2-7.2.295
- David A. Towers and Vicente R. Varea, Elementary Lie algebras and Lie $A$-algebras, J. Algebra 312 (2007), no.ย 2, 891โ901. MR 2333190, DOI 10.1016/j.jalgebra.2006.11.034
Additional Information
- Kristen Stagg
- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
- Email: klstagg@ncsu.edu
- Ernest Stitzinger
- Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
- Email: stitz@math.ncsu.edu
- Received by editor(s): January 28, 2010
- Received by editor(s) in revised form: July 16, 2010
- Published electronically: December 23, 2010
- Communicated by: Gail R. Letzter
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2435-2437
- MSC (2010): Primary 17B30
- DOI: https://doi.org/10.1090/S0002-9939-2010-10711-6
- MathSciNet review: 2784809