Abstract
We study the class of groups $G$ satisfying the condition that, for every ordered pair $x,y \in G$, one of the following is true: (1)~$xy=yx$; (2)~$x$ and $y$ are conjugate; (3)~$x^y=x^{-1}$; (4)~$y^x=y^{-1}$. We describe all such groups completely and give a further condition that characterizes these groups in terms of their $3$-$\text{S}$-rings.
Citation
Stephen P. Humphries. Emma L. Rode. "A class of groups determined by their $3$-$\text{S}$-rings." Rocky Mountain J. Math. 45 (2) 565 - 581, 2015. https://doi.org/10.1216/RMJ-2015-45-2-565
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