Finite groups with a certain number of cyclic subgroups II

TL;DR

This paper characterizes finite groups with exactly |G|-2 cyclic subgroups, advancing understanding of subgroup structures in finite group theory.

Contribution

It provides a partial classification of finite groups with a specific number of cyclic subgroups, addressing an open problem from prior research.

Findings

Finite groups with |G|-2 cyclic subgroups are characterized.

The work partially solves an open problem in the classification of finite groups.

Provides structural insights into groups with a near-maximal number of cyclic subgroups.

Abstract

In this note we describe the finite groups $G$ having $|G|-2$ cyclic subgroups. This partially solves the open problem in the end of \cite{3}.