Graded lie algebras of maximal class

Transactions of the American Mathematical Society

Volumn 349, Issue 10, 1997, Pages 4021-4051

  Caranti, A ^a   Mattarei, S ^a   Newman, M F ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Graded lie algebras of maximal class; Nilpotent lie algebras; P groups of maximal class; Pro p groups of finite coclass

Indexed keywords

EID: 21944441888     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-02005-9     Document Type: Article

References (17)

1. [AF] A. A. Albert and M. S. Frank, Simple Lie algebras of characteristic p, Rend. Sem. Mat. Univ. Politec. Torino 14 (1954/5), 117-139. MR 18:52a
2. [Bla] N. Blackburn, On a special class of p-groups, Acta Math. 100 (1958), 45-92. MR 21:1349
3. [Bio] Richard E. Block, Determination of the differentiably simple rings with a minimal ideal, Ann. of Math. 90 (1969), 433-459. MR 40:4319
4. [CMNS] A. Garanti, S. Mattarei, M. F. Newman and C. M. Scoppola, Thin groups of prime-power order and thin Lie algebras, Quart. J. Math. Oxford Ser. (2) 47 (1996), 279-296. CMP 97:02
5. [CN3] F. Celler, M. F. Newman, W. Nickel and A. C. Niemeyer, An algorithm for computing quotients of prime-power order for finitely presented groups and its implementation in GAP, Research Report 127, Australian National University, Canberra, 1993.
6. [HNO] George Havas, M.F. Newman and E.A. O'Brien, ANU p-Quotient Program (Version 1.2), written in C, available from maths.anu.edu.au by anonymous ftp in the directory pub/PQ, as a share library with GAP 3.4 and as part of Magma, 1995.
7. [Hu] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1967. MR 37:302
8. [Jac] Nathan Jacobson, Lie algebras, Dover, New York, 1979. MR 80k:17001
9. Edouard Lucas, Sur les congruences des nombres eulériens et des coefficients différentiels des fonctions trigonométriques, suivant un module premier, Bull. Soc. Math. France 6 (1878), 49-54.
10. [Ma] Avinoam Mann, Space groups and groups of prime power order. VII. Powerful p-groups and uncovered p-groups, Bull. London Math. Soc. 24 (1992), 271-276. MR 93c:20041
11. [M2] S. McKay, On the structure of a special class of p-groups II, Quart. J. Math. Oxford Ser. (2) 41 (1990), 431-448. MR 91k:20027
12. [S+] Martin Schönert et al., GAP - Groups, Algorithms, and Programming, Release 3.4, Lehrstuhl D für Mathematik, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany, 1995.
13. [Shl] Aner Shalev, The structure of finite p-groups: constructive proof of the coclass conjectures, Invent. Math. 115 (1994), 315-345. MR 95j:20022b
14. [Sh2] Aner Shalev, Simple Lie algebras and Lie algebras of maximal class, Arch. Math. (Basel) C3 (1994), 297-301. MR 95j:17025
15. [Sh3] Aner Shalev, Finite p-groups, Proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups, Istanbul, Turkey, 1994, NATO ASI Series, vol. 471, Kluwer Academic Publishers, Dordrecht/Boston/London, 1995, pp. 401-450. MR 96f:20002
16. [SZ] Aner Shalev and E. I. Zelmanov, Narrow Lie algebras I: a coclass theory and a characterization of the Witt algebra, 3. Algebra 189 (1997), 294-330.
17. [Z] Hans Zassenhaus, Über Liesche Ringe mit Primzahlcharakteristik, Abh. Math. Sem. Univ. Hamburg 13 (1939), 1-100.