On the Total Dominating Set of ${3}/{2}$-Generated Groups

Authors

  • Varujan Atabekyan Yerevan State University
  • Haik Aslanyan American University of Armenia

DOI:

https://doi.org/10.52737/18291163-2024.16.10-1-7

Keywords:

Spred of Group, Total Dominating Set, 3/2-generated Group, Tarski Monster

Abstract

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.

References

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Published

2024-10-01

How to Cite

On the Total Dominating Set of ${3}/{2}$-Generated Groups. (2024). Armenian Journal of Mathematics, 16(10), 1-7. https://doi.org/10.52737/18291163-2024.16.10-1-7