Groups whose Chermak-Delgado lattice is a quasi-antichain

2017/05/18 by Lijian An, An, Lijian
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1705.06456

openalex publication_date 2017/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 (≥ 3), a quasiantichain of width w is denoted by M_w. In \citeBHW2, it is proved that M_w can be as a Chermak-Delgado lattice of a finite group if and only if w=1+p^a for some positive integer a. Let t be the number of abelian atoms in CD(G). If t>2, then, according to \citeBHW2, there exists a positive integer b such that t=p^b+1. The converse is still an open question. In this paper, we proved that a=b or a=2b.

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