Power sets and soluble subgroups
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- by Martin W. Liebeck and Aner Shalev PDF
- Proc. Amer. Math. Soc. 142 (2014), 3757-3760 Request permission
Abstract:
We prove that for certain positive integers $k$, such as 12, a normal subgroup of a finite group which consists of $k^{th}$ powers is necessarily soluble. This gives rise to new solubility criteria, and solves an open problem from a 2013 paper by the authors.References
- E. Hrushovski, P. H. Kropholler, A. Lubotzky, and A. Shalev, Powers in finitely generated groups, Trans. Amer. Math. Soc. 348 (1996), no. 1, 291–304. MR 1316851, DOI 10.1090/S0002-9947-96-01456-0
- Martin W. Liebeck and Aner Shalev, Powers in finite groups and a criterion for solubility, Proc. Amer. Math. Soc. 141 (2013), no. 12, 4179–4189. MR 3105861, DOI 10.1090/S0002-9939-2013-11790-9
Additional Information
- Martin W. Liebeck
- Affiliation: Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom
- MR Author ID: 113845
- ORCID: 0000-0002-3284-9899
- Aner Shalev
- Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
- MR Author ID: 228986
- ORCID: 0000-0001-9428-2958
- Received by editor(s): December 20, 2012
- Published electronically: July 24, 2014
- Additional Notes: The authors are grateful for the support of an EPSRC grant
The second author acknowledges the support of Advanced ERC Grant 247034, an ISF grant 754/08, and the Miriam and Julius Vinik Chair in Mathematics, which he holds. - Communicated by: Pham Huu Tiep
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 3757-3760
- MSC (2010): Primary 20D10, 20E07, 20D06
- DOI: https://doi.org/10.1090/S0002-9939-2014-12203-9
- MathSciNet review: 3251717