7 papers
Recovering information about a finite group from its subrack lattice
Selçuk Kayacan
We prove that the isomorphism type of the subrack lattice of a finite group determines the nilpotence class. We analyze the problem of estimating the orders of the group elements c…
On a conjecture about profiles of finite connected racks
Selçuk Kayacan
A rack is a set with a binary operation such that left multiplications are automorphisms of the set and a quandle is a rack satisfying a certain condition. For a finite connected r…
Some remarks on the subrack lattice of finite racks
Selçuk Kayacan
The set of all subracks of a finite rack form a lattice under inclusion. We prove that if a rack satisfies a certain condition then the homotopy type of th…
Dominating Sets in Intersection Graphs of Finite Groups
Selçuk Kayacan
Let be a group. The intersection graph of is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-tri…
-free Intersection Graphs of Finite Groups
Selçuk Kayacan
The intersection graph of a group is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of $…
Connectivity of Intersection Graphs of Finite Groups
Selçuk Kayacan
The intersection graph of a group is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of $…
Abelian Groups With Isomorphic Intersection Graphs
Ergün Yaraneri
Let G be a group. The intersection graph G(G) of G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial su…