@article{On the Total Dominating Set of ${3}/{2}$-Generated Groups_2024, volume={16}, url={https://armjmath.sci.am/index.php/ajm/article/view/1179}, DOI={10.52737/18291163-2024.16.10-1-7}, abstractNote={
A subset $S$ of a group $G$ is called a total dominating set of $G$ if for any nontrivial element $x\in G$ there is an element $y\in S$ such that $G =\left< x, y\right> $. Tarski monsters, constructed by Olshanskii, are infinite simple groups, any pair of non-commuting elements of which is a total dominating set. In this paper, we construct an infinite non-cyclic and non-simple group having a total dominating set from two elements. This gives a positive answer to Donoven and Harper’s question about the existence of infinite groups (other than Tarski monsters) having a finite total dominating set. In addition, our examples have an infinite uniform spread.
}, number={10}, journal={Armenian Journal of Mathematics}, year={2024}, month={Oct.}, pages={1–7} }