Scott Harper

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20182020

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7 papers · 1 filter

math.GR2020

Shintani descent, simple groups and spread

Scott Harper

The spread of a group $G$ , written $s (G)$ , is the largest $k$ such that for any nontrivial elements $x_{1}, \dots, x_{k} \in G$ there exists $y \in G$ such that $G = \langle x_i, y \ra…

math.GR2020

The spread of a finite group

Timothy C. Burness, Robert M. Guralnick, Scott Harper

A group $G$ is said to be $\frac{3}{2}$ -generated if every nontrivial element belongs to a generating pair. It is easy to see that if $G$ has this property then every proper quotie…

math.GR2020

The Spread of Almost Simple Classical Groups

Scott Harper

Every finite simple group can be generated by two elements, and in 2000, Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group every n…

math.GR2020

Connectivity of generating graphs of nilpotent groups

Scott Harper, Andrea Lucchini

Let $G$ be $2$ -generated group. The generating graph of $Γ (G)$ is the graph whose vertices are the elements of $G$ and where two vertices $g$ and $h$ are adjacent if $G=\langle g,h…

math.GR2019

Infinite $\frac{3}{2}$ -generated groups

Casey Donoven, Scott Harper

Every finite simple group can be generated by two elements, and Guralnick and Kantor proved that, moreover, every nontrivial element is contained in a generating pair. Groups with…

math.GR2018

Finite groups, 2-generation and the uniform domination number

Timothy C. Burness, Scott Harper

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 $x_{1}, \dots, x_{k}$ , there exists $y \in G$ su…

Shintani descent, simple groups and spread

The spread of a finite group

The Spread of Almost Simple Classical Groups

Connectivity of generating graphs of nilpotent groups

Infinite 23​-generated groups

Finite groups, 2-generation and the uniform domination number

Infinite $\frac{3}{2}$ -generated groups