A factorization theorem for groups and Lie algebras

Author:
Eugene Schenkman

Journal:
Proc. Amer. Math. Soc. **68** (1978), 149-152

MSC:
Primary 17B60; Secondary 20F05

MathSciNet review:
0469996

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A proof is given for a generalization of a theorem of Mennicke that each member of a certain family of groups defined by generators and relations is finite. This leads to the following theorem on factorization of groups.

Theorem. *Let G be generated by abelian subgroups A, B, C, such that* ; *then the second derived group*, *is nilpotent of class at most* 3.

Also proved is the analogue of the above theorem for Lie algebras.

**[1]**Jens Mennicke,*Einige endliche Gruppen mit drei Erzeugenden und drei Relationen*, Arch. Math. (Basel)**10**(1959), 409–418 (German). MR**0113946****[2]**Eugene Schenkman,*Group theory*, Robert E. Krieger Publishing Co., Huntington, N.Y., 1975. Corrected reprint of the 1965 edition. MR**0460422**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
17B60,
20F05

Retrieve articles in all journals with MSC: 17B60, 20F05

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1978-0469996-4

Keywords:
Generators,
relations,
factorization,
abelian subgroup,
abelian subalgebras,
derived subgroup,
derived subalgebra,
nilpotent

Article copyright:
© Copyright 1978
American Mathematical Society