A factorization theorem for groups and Lie algebras
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- by Eugene Schenkman PDF
- Proc. Amer. Math. Soc. 68 (1978), 149-152 Request permission
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 $[A,B] \leqslant A,[B,C] \leqslant B,[C,A] \leqslant C$; then the second derived group, $G''$ is nilpotent of class at most 3. Also proved is the analogue of the above theorem for Lie algebras.References
- Jens Mennicke, Einige endliche Gruppen mit drei Erzeugenden und drei Relationen, Arch. Math. (Basel) 10 (1959), 409–418 (German). MR 113946, DOI 10.1007/BF01240820
- Eugene Schenkman, Group theory, Robert E. Krieger Publishing Co., Huntington, N.Y., 1975. Corrected reprint of the 1965 edition. MR 0460422
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 149-152
- MSC: Primary 17B60; Secondary 20F05
- DOI: https://doi.org/10.1090/S0002-9939-1978-0469996-4
- MathSciNet review: 0469996