39 citations · 72 across the 24 of their papers we have counts for
4 papers · 1 filter
Limit points in the range of the commuting probability function on finite groups
Peter Hegarty
If G is a finite group, then Pr(G) denotes the fraction of ordered pairs of elements of G which commute. We show that, if l \in (2/9,1] is a limit point of the function Pr on finit…
Can connected commuting graphs of finite groups have arbitrarily large diameter ?
Peter Hegarty, Dmitry Zhelezov
We present a family of finite, non-abelian groups and propose that there are members of this family whose commuting graphs are connected and of arbitrarily large diameter. If true,…
Minimal odd order automorphism groups
Peter Hegarty, Desmond MacHale
We show that 3^7 is the smallest order of a non-trivial odd order group which occurs as the full automorphism group of a finite group.
Finite groups with an automorphism cubing a large fraction of elements
Peter Hegarty
We investigate the possible structures imposed on a finite group by its possession of an automorphism sending a large fraction of the group elements to their cubes, the philosophy…