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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lifting of generating subgroups


Author: Ido Efrat
Journal: Proc. Amer. Math. Soc. 125 (1997), 2217-2219
MSC (1991): Primary 20D99
MathSciNet review: 1401738
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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 $\varphi (G_{i}^{g_{i}})=H_{i}$, $i=1 ,\ldots ,n$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03917-8
PII: S 0002-9939(97)03917-8
Received by editor(s): February 13, 1996
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society