The lower central series of the group ⟨𝑥,𝑦: 𝑥^{𝑝}=1⟩

Labute, John P.

doi:10.1090/S0002-9939-1977-0480751-0

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Browser Compatibility Info Help
ISSN 1088-6826(online) ISSN 0002-9939(print)

The lower central series of the group $\langle x, y:$ $x\sp{p}=1\rangle$

Author: John P. Labute
Journal: Proc. Amer. Math. Soc. 66 (1977), 197-201
MSC: Primary 20E30; Secondary 17B30
MathSciNet review: 0480751
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we determine the Lie algebra associated to the lower central series of the group $\langle x,y:{x^p} = 1\rangle$ , p a prime.

[1] N. Bourbaki, Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie, Hermann, Paris, 1972. Actualités Scientifiques et Industrielles, No. 1349. MR 0573068 (58 #28083a)
[2] Anthony M. Gaglione, Factor groups of the lower central series for special free products, J. Algebra 37 (1975), no. 1, 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] John P. Labute, Algèbres de Lie et pro-𝑝-groupes définis par une seule relation, Invent. Math. 4 (1967), 142–158 (French). MR 0218495 (36 #1581)
[5] John P. Labute, On the descending central series of groups with a single defining relation, J. Algebra 14 (1970), 16–23. MR 0251111 (40 #4342)
[6] John P. Labute, Free Lie algebras as modules over their enveloping algebras, Proc. Amer. Math. Soc. 68 (1978), no. 2, 135–139. MR 0469992 (57 #9770), http://dx.doi.org/10.1090/S0002-9939-1978-0469992-7
[7] Michel Lazard, Sur les groupes nilpotents et les anneaux de Lie, Ann. Sci. Ecole Norm. Sup. (3) 71 (1954), 101–190 (French). MR 0088496 (19,529b)
[8] Michel Lazard, Groupes analytiques 𝑝-adiques, Inst. Hautes Études Sci. Publ. Math. 26 (1965), 389–603 (French). 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.

Bibliography