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

2021/07/07 by Lijian An, An, Lijian
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2107.03108

openalex publication_date 2021/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 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.

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