Large subgroups of a finite group of even order
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- by Bernhard Amberg and Lev Kazarin PDF
- Proc. Amer. Math. Soc. 140 (2012), 65-68 Request permission
Abstract:
It is shown that if $G$ is a group of even order with trivial center such that $|G|>2|C_{G}(t)|^{3}$ for some involution $t\in G$, then there exists a proper subgroup $H$ of $G$ such that $|G|< |H|^{2}$. If $|G|>|C_{G}(t)|^{3}$ and $k(G)$ is the class number of $G$, then $|G|\leq k(G)^{3}$.References
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Additional Information
- Bernhard Amberg
- Affiliation: Fachbereich Mathematik, Universität Mainz, D-55099 Mainz, Germany
- Email: amberg@mathematik.uni-mainz.de
- Lev Kazarin
- Affiliation: Department of Mathematics, Yaroslavl State University, 150000 Yaroslavl, Russia
- Email: kazarin@uniyar.ac.ru
- Received by editor(s): November 3, 2010
- Published electronically: May 10, 2011
- Additional Notes: The second author is grateful to the Department of Mathematics of the University of Mainz for its warm hospitality during the time when this reseach was done. He would also like to thank the Deutsche Forschungsgemeinschaft for its financial support.
- Communicated by: Jonathan I. Hall
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 65-68
- MSC (2010): Primary 20D05, 20D06
- DOI: https://doi.org/10.1090/S0002-9939-2011-10982-1
- MathSciNet review: 2833517