Finite p-groups with at most p2 + p subgroups not in Chermak-Delgado lattice

TL;DR

This paper characterizes finite p-groups based on the number of subgroups outside their Chermak-Delgado lattice, identifying those with at most p^2 + p such subgroups.

Contribution

It provides a classification of finite p-groups with a bounded number of subgroups outside the Chermak-Delgado lattice, a novel structural insight.

Findings

Finite p-groups with at most p^2 + p subgroups outside the Chermak-Delgado lattice are characterized.

The paper establishes bounds on the number of subgroups not in the Chermak-Delgado lattice.

Structural properties of these p-groups are elucidated.

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 determine finite p-groups with at most p2 + p subgroups not in Chermak-Delgado lattice.