The lower central series of the group
Author:
John P. Labute
Journal:
Proc. Amer. Math. Soc. 66 (1977), 197-201
MSC:
Primary 20E30; Secondary 17B30
DOI:
https://doi.org/10.1090/S0002-9939-1977-0480751-0
MathSciNet review:
0480751
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we determine the Lie algebra associated to the lower central series of the group , p a prime.
- [1] N. Bourbaki, Éléments de mathématique. Groupes et algèbres de Lie, Chapter 2, Hermann, Paris, 1972. MR 0573068 (58:28083a)
- [2] A. Gaglione, Factor groups of the lower central series for special free products, J. Algebra 37 (1975), 172-185. MR 0384933 (52:5803)
- [3] P. Hall, A contribution to the theory of groups of prime power order, Proc. London Math. Soc. 36 (1934), 29-95.
- [4] J. Labute, Algèbres de Lie et pro-p-groupes définis par une seule relation, Invent. Math. 4 (1967), 142-158. MR 36 #1581. MR 0218495 (36:1581)
- [5] -, On the descending central series of groups with a single defining relation, J. Algebra 4 (1970), 16-23. MR 40 #4342. MR 0251111 (40:4342)
- [6] -, Free Lie algebras as modules over their enveloping algebras, Proc. Amer. Math. Soc. (to appear). MR 0469992 (57:9770)
- [7] M. Lazard, Sur les groupes nilpotents et les anneaux de Lie, Ann. Ecole Norm. Sup. 71 (1954), 101-190. MR 19, 529. MR 0088496 (19:529b)
- [8] -, Groupes analytiques p-adiques, Inst. Hautes Études Sci. Publ. Math. No. 26 (1965), 389-603. MR 35 #188. MR 0209286 (35:188)
- [9] A. Magnus, A. Karass and D. Solitar, Combinatorial group theory, Pure and Appl. Math., Vol. 13, Interscience, New York, 1966. MR 34 #7617.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1977-0480751-0
Keywords:
One relator group,
lower central series,
Lie algebra
Article copyright:
© Copyright 1977
American Mathematical Society