A factorization theorem for groups and Lie algebras
Proc. Amer. Math. Soc. 68 (1978), 149-152
Primary 17B60; Secondary 20F05
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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.
- J. Mennicke, Einige endliche Gruppen mit drei Erzeugenden und drei Relationen, Arch. Math. (Basel) 10 (1959), 409-418. MR 0113946 (22:4777)
- Eugene Schenkman, Group theory, Krieger, Huntington, N.Y., 1975. MR 0460422 (57:416)
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