Lifting of generating subgroups
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Abstract:
Let $\varphi \colon G\to H$ be an epimorphism of finite groups. Suppose that $G$ is generated by its subgroups $G_{1} ,\ldots ,G_{n}$ and that $H$ is generated by its subgroups $H_{1},\ldots ,H_{n}$. Furthermore, suppose that $\varphi (G_{i})$ and $H_{i}$ are conjugate, $i=1,\ldots ,n$. We prove that there exist $g_{1},\ldots ,g_{n}\in G$ such that $G_{1}^{g_{1}} ,\ldots ,G_{n}^{g_{n}}$ generate $G$ and $\varphi (G_{i}^{g_{i}})=H_{i}$, $i=1 ,\ldots ,n$.References
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Additional Information
- Ido Efrat
- Affiliation: Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, P.O. Box 653, Be’er-Sheva 84105, Israel
- Email: efrat@math.bgu.ac.il
- Received by editor(s): February 13, 1996
- Communicated by: Ronald M. Solomon
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2217-2219
- MSC (1991): Primary 20D99
- DOI: https://doi.org/10.1090/S0002-9939-97-03917-8
- MathSciNet review: 1401738