Related papers: Some Groups with Computable Chermak-Delgado Lattic…

For a finite group G with subgroup H the Chermak-Delgado measure of H in G refer to the product of the order of H with the order of its centralizer, C_G(H). The set of all subgroups with maximal Chermak-Delgado measure form a sublattice,…

In a finite group G with subgroup H, the Chermak-Delgado measure of H (in G) is defined as the product of the order of H with the order of the centralizer of H. The Chermak-Delgado lattice of G, denoted CD(G), is the set of all subgroups…

The Chermak-Delgado lattice of a finite group is a modular, self-dual sublattice of the lattice of subgroups of $G$. The least element of the Chermak-Delgado lattice of $G$ is known as the Chermak-Delgado subgroup of $G$. This paper…

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 contains the product of the Chermak-Delgado lattices of the…

Given a finite group $G$, we denote by $L(G)$ the subgroup lattice of $G$ and by ${\cal CD}(G)$ the Chermak-Delgado lattice of $G$. In this note, we determine the finite groups $G$ such that $|{\cal CD}(G)|=|L(G)|-k$, $k=1,2$.

Let $G$ be a finite group and $H\leq G$. The Chermak-Delgado measure of $H$ is defined as the number $|H|\cdot|C_{G}(H)|$. In this paper, we identify finite groups that exhibit the maximum number of Chermak-Delgado measures under some…

In this note we describe the structure of finite groups G whose Chermak-Delgado lattice is the interval [G/Z(G)] = {H \in L(G) \mid Z(G)\leq H\leq G}.

The Chermak-Delgado lattice of a finite group $G$ is a self-dual sublattice of the subgroup lattice of $G$. In this paper, we focus on finite groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian $p$-group. We…

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 of the group. This is our main result. We use this result…

It is an open question in the study of Chermak-Delgado lattices precisely which finite groups $G$ have the property that $CD(G)$ is a chain of length $0$. In this note, we determine two classes of groups with this property. We prove that if…

A group $G$ is said to have dense ${\cal CD}$-subgroups if each non-empty open interval of the subgroup lattice $L(G)$ contains a subgroup in the Chermak--Delgado lattice ${\cal CD}(G)$. In this note, we study finite groups satisfying this…

The Chermak-Delgado lattice of a finite group G is a self-dual sublattice of the subgroup lattice of G. In this paper, we determine finite p-groups with at most p2 + p subgroups not in Chermak-Delgado lattice.

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 the Chermak-Delgado measure of a group is actually a map of…

In this short note, we describe finite groups all of whose non-trivial cyclic subgroups have the same Chermak-Delgado measure.

The Chermak-Delgado lattice of a finite group is a dual, modular sublattice of the subgroup lattice of the group. This paper considers groups with a quasi-antichain interval in the Chermak-Delgado lattice, ultimately proving that if there…

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 subgroups with many intriguing properties. Fasol\u{a} and…

For a finite group G, we denote by v(G) the number of conjugacy classes of subgroups of G not in CD(G). In this paper, we determine the finite groups G such that v(G)=1,2,3.

Given the large class of groups already known to be sofic, there is seemingly a shortfall in results concerning their permanence properties. We address this problem for wreath products, and in particular investigate the behaviour of more…

Let G be a totally disconnected, locally compact group. A closed subgroup of G is locally normal if its normaliser is open in G. We begin an investigation of the structure of the family of closed locally normal subgroups of G. Modulo…

A quasiantichain is a lattice consisting of a maximum, a minimum, and the atoms of the lattice. The width of a quasiantichian is the number of atoms. For a positive integer $w$ ($\ge 3$), a quasiantichain of width $w$ is denoted by…