1 citations · 1 across the 8 of their papers we have counts for
9 papers
Some answers regarding factorizations of finite groups
Ryan McCulloch
In this note we answer some questions of G. M. Bergman concerning factorizations of finite groups. Such questions originated when M. H. Hooshmand asked whether, given a finite grou…
An answer regarding automorphisms of finite abelian groups
Ryan McCulloch
In this note we provide a negative answer to the question: ``Is it true that for every positive rational number there exists a finite abelian group such that $|\mathrm{Aut}…
Covering by Centralizers
Mark L. Lewis, Ryan McCulloch
In this paper, we consider covers of finite groups by centralizers of elements. We show that the set of centralizers that are maximal under the partial ordering form a cover of the…
A Möbius function on the centralizer lattice
William Cocke, Mark L. Lewis, Ryan McCulloch
We consider the Möbius function on the poset of element centers and obtain some new results regarding centralizers in a -group.
The commuting graph and a graph associated with centralizers
Mark L. Lewis, Ryan McCulloch
Let be a -group. We begin to consider the relationship between the structure of the commuting graph and . We also build a family of groups whose commuting graphs h…
The Cycle Counts of Graphs
Ryan McCulloch, Brendan D. McKay, Alireza Salahshoori +1
We prove that an inseparable graph can have any positive number of cycles with the six exceptions 2, 4, 5, 8, 9, 16, and that an inseparable cubic graph has the additional exceptio…
Finite groups with dense -subgroups
Ryan McCulloch, Marius Tărnăuceanu
A group is said to have dense -subgroups if each non-empty open interval of the subgroup lattice contains a subgroup in the Chermak--Delgado lattice ${\cal CD…
Incidence Gain Graphs and Generalized Quadrangles
Ryan McCulloch
We demonstrate a construction method based on a gain function that is defined on the incidence graph of an incidence geometry. Restricting to when the incidence geometry is a linea…
Locally resolvable BIBDs and generalized quadrangles with ovoids
Ryan McCulloch
In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that posses a non-tria…