13 citations · 40 across the 9 of their papers we have counts for
9 papers
The category of centralizer lattices of groups
William Cocke, Mark L. Lewis, Ryan McCulloch
We formalize the concept of a centralizer-respecting homomorphism, surjective homomorphisms which are equivariant with respect to taking the centralizer of a subgroup. There is a f…
Finite groups with many elements of the same order
Ryan McCulloch, Lee Tae Young
We study a conjecture by Deaconescu on the solubility of finite groups with claims that if more than half of the elements in a finite group has the same order , then the group i…
On the Chermak-Delgado lattice of a finite group
Ryan McCulloch, Marius Tărnăuceanu
By imposing conditions upon the index of a self-centralizing subgroup of a group, and upon the index of the center of the group, we are able to classify the Chermak-Delgado lattice…
The Chermak-Delgado Measure as a Map on Posets
William Cocke, Ryan McCulloch
The Chermak-Delgado measure of a finite group is a function which assigns to each subgroup a positive integer. In this paper, we give necessary and sufficient conditions for when t…
On groups with few subgroups not in the Chermak-Delgado lattice
David Burrell, William Cocke, Ryan McCulloch
We investigate the question of how many subgroups of a finite group are not in its Chermak-Delgado lattice. The Chermak-Delgado lattice for a finite group is a self-dual lattice of…
Central Products and the Chermak-Delgado Lattice
William Cocke, Ryan McCulloch
The Chermak-Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups. We prove that the Chermak-Delgado lattice of a central product contain…
Two classes of finite groups whose Chermak-Delgado lattice is a chain of length zero
Ryan McCulloch, Marius Tărnăuceanu
It is an open question in the study of Chermak-Delgado lattices precisely which finite groups have the property that is a chain of length . In this note, we determin…
Finite Groups with a Trivial Chermak-Delgado Subgroup
Ryan McCulloch
The Chermak-Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups of . The least element of the Chermak-Delgado lattice of is know…
Chermak-Delgado Simple Groups
Ryan McCulloch
This paper provides the first steps in classifying the finite solvable groups having Property A, which is a property involving abelian normal subgroups. We see that this classifica…