2014/07/23 by Ben Brewster, Brewster, Ben, Peter Hauck +3
Computer Science · Mathematics · #20D30 #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR #msc:20D30
paper · pdf · doi:10.48550/arxiv.1407.6215
11 pages
arxiv created 2014/07/23 · openalex publication_date 2014/07/23 · arxiv updated 2014/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 is a quasi-antichain interval between L and H with L ≤ H then there exists a prime p such that the quotient H / L is an elementary abelian p-group and the number of atoms in the quasi-antichain is one more than a power of p. In the case where the Chermak-Delgado lattice of the entire group is a quasi-antichain, the relationship between the number of abelian atoms and the prime p is examined; additionally several examples of group with a quasi-antichain Chermak-Delgado lattice are constructed.