6 citations · 8 across the 8 of their papers we have counts for
16 papers
Generating simple vigorous groups
Collin Bleak, Casey Donoven, Scott Harper +1
The simple vigorous groups form a broad class of groups of homeomorphisms of Cantor space that includes Thompson's group , its various generalisations and many others such as Ne…
Totally deranged elements of almost simple groups and invariable generating sets
Scott Harper
By a classical theorem of Jordan, every faithful transitive action of a nontrivial finite group has a derangement (an element with no fixed points). The existence of derangements w…
The maximal size of a minimal generating set
Scott Harper
A generating set for a finite group is said to be minimal if no proper subset generates , and denotes the maximal size of a minimal generating set for . We prove a…
The spread of finite and infinite groups
Scott Harper
It is well known that every finite simple group has a generating pair. Moreover, Guralnick and Kantor proved that every finite simple group has the stronger property, known as $\fr…
Thompson's group is -generated
Collin Bleak, Scott Harper, Rachel Skipper
Every finite simple group can be generated by two elements and, in fact, every nontrivial element is contained in a generating pair. Groups with this property are said to be $\frac…
Flexibility in generating sets of finite groups
Scott Harper
Let G be a finite group. It has recently been proved that every nontrivial element of G is contained in a generating set of minimal size if and only if all proper quotients of G re…