Finite groups, 2-generation and the uniform domination number

@article{Burness2018FiniteG2,
  title={Finite groups, 2-generation and the uniform domination number},
  author={Timothy C. Burness and Scott Harper},
  journal={arXiv: Group Theory},
  year={2018}
}
Let $G$ be a finite $2$-generated non-cyclic group. The spread of $G$ is the largest integer $k$ such that for any nontrivial elements $x_1, \ldots, x_k$, there exists $y \in G$ such that $G = \langle x_i, y\rangle$ for all $i$. The more restrictive notion of uniform spread, denoted $u(G)$, requires $y$ to be chosen from a fixed conjugacy class of $G$, and a theorem of Breuer, Guralnick and Kantor states that $u(G) \geqslant 2$ for every non-abelian finite simple group $G$. For any group with… Expand
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