Corpus ID: 235755477

# Groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian $p$-group

@inproceedings{An2021GroupsWC,
title={Groups whose Chermak-Delgado lattice is a subgroup lattice of an elementary abelian \$p\$-group},
author={Lijian An},
year={2021}
}
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 ChermakDelgado lattice is a subgroup lattice of an elementary abelian p-group. We prove that such groups are nilpotent of class 2. We also prove that, for any elementary abelian p-group E, there exists a finite group G such that the Chermak-Delgado lattice of G is a subgroup lattice of E.

#### References

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• Mathematics
• 2018
ABSTRACT 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 classesExpand
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• Mathematics
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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–DelgadoExpand
Groups Whose Chermak-Delgado Lattice is a Chain
• Mathematics
• 2013
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 maximalExpand
Finite groups with a trivial Chermak–Delgado subgroup
Abstract 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 theExpand
ABSTRACT 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 classification isExpand
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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}.
• Mathematics
• 2013
If G is a finite group with subgroup H, then the Chermak–Delgado measure of H (in G) is defined as |H||C G (H)|. The Chermak–Delgado lattice of G, denoted 𝒞𝒟(G), is the set of all subgroups withExpand
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• Mathematics
• Bulletin of the Australian Mathematical Society
• 2012
Abstract Let G be a finite group and let H≤G. We refer to |H||CG(H)| as the Chermak–Delgado measure ofH with respect to G. Originally described by Chermak and Delgado, the collection of all subgroupsExpand
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• Mathematics
• 2018
Abstract Let G be a finite group and let H ≤ G . The Chermak–Delgado measure ( [7] ) of H is defined as the number | H ‖ C G ( H ) | . The subgroups of G having maximum measure, the F 1 ( G )Expand
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