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Finite groups in which elements of the same order outside the center are conjugate

Guohua Qian·Wujie Shi·Xingzhong You
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Abstract

In this paper, we prove that if $G$ is a finite group in which elements of the same order outside the center are conjugate, then $G$ is abelian or is isomorphic to $S_3$, the symmetry group of degree 3.

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Guohua Qian, Wujie Shi, Xingzhong You. 2005-09-15. Finite groups in which elements of the same order outside the center are conjugate. https://arxiv.org/abs/math/0509351

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