Abstract
Let G be a finite group and e a positive integer dividing |G|, the order of G. Denoting \({L_e(G)=\{x\in G|\,x^e=1\}}\) , Frobenius proved that |L e (G)| = ke for a positive integer k ≥ 1. In this paper, we give a complete classification of finite groups G with |L e (G)| ≤ 2e for every e dividing |G|.
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W. Meng was supported by the Science Research Foundation of Department of Education of Yunnan Province (2010Y432) and the Tianyuan Fund for Mathematics of the National Natural Science Foundation of China (11026204); the second author was supported by China Postdoctoral Science Foundation (20100470136).
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Meng, W., Shi, J. On an inverse problem to Frobenius’ theorem. Arch. Math. 96, 109–114 (2011). https://doi.org/10.1007/s00013-010-0211-4
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DOI: https://doi.org/10.1007/s00013-010-0211-4