Related papers: Finite groups with small number of cyclic subgroup…

We study the number of cylic subgroups in finite groups and get that $G$ has $|G|-3$ cyclic subgroups if and only if $G \cong D_{10}$ or $Q_8$.

In this short note, we describe the finite groups $G$ having $|G|-1$ cyclic subgroups. This leads to a nice characterization of the symmetric group $S_3$.

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}.

In this note, we classify all finite groups having exactly 6, 7 or 8 cyclic subgroups. This gives a partial answer to the open problem posed by Tarnauceanu (Amer. Math. Monthly, 122 (2015), 275-276). As a consequence of our results, we also…

Marius T\u{a}rn\u{a}uceanu described the finite groups $G$ having $|G|-1$ cyclic subgroups. We describe the finite groups $G$ having $|G|-\Delta$ cyclic subgroups for $\Delta=2, 3, 4$ and $5$.

In this note, we show that among finite nilpotent groups of a given order or finite groups of a given odd order, the cyclic group of that order has the minimum number of edges in its cyclic subgroup graph. We also conjecture that this holds…

In this paper we introduce and study the relative cyclic subgroup commutativity degrees of a finite group. We show that there is a finite group with $n$ such degrees for all $n \in \mathbb{N}^*\setminus \lbrace 2\rbrace$ and we indicate…

We determine the structure of the finite groups with the property that every cyclic subgroup is the intersection of maximal subgroups, comparing this property with the one where all proper subgroups are intersections of maximal subgroups.

In this paper, we classify the finite simple groups with an abelian Sylow subgroup.

A finite group is said to be $n$-cyclic if it contains $n$ cyclic subgroups. For a finite group $G$, the ratio of the number of cyclic subgroups to the number of subgroups is known as the cyclicity degree of the group $G$ and is denoted by…

Let $G$ be a finite group, $L_1(G)$ be its poset of cyclic subgroups and consider the quantity $\alpha(G)=\frac{|L_1(G)|}{|G|}$. The aim of this paper is to study the class $\cal{C}$ of finite nilpotent groups having…

Recent results of Qu and Tuarnauceanu describe explicitly the finite p-groups which are not elementary abelian and have the property that the number of their subgroups is maximal among p-groups of a given order. We complement these results…

In this short note, we describe finite groups all of whose non-trivial cyclic subgroups have the same Chermak-Delgado measure.

Let $G$ be a finite group, define $I(G)=\{x\in G : x^{2}=1\}$, $C(G)=$ set of the cyclic subgroups of $G$, $i(G)=|I(G)|$ and $c(G)=|C(G)|$. In this article, we will classify finite groups with $i(G)=c(G)-r$ for $r=0,1,$ and $2$. We also…

T\u{a}rn\u{a}uceanu described the finite groups $G$ having exactly $|G|-1$ cyclic subgroups. In "Finite Groups with a Prescribed Number of Cyclic Subgroups,", we used elementary methods to completely characterize those finite groups $G$…

For a finite group G, we denote by v(G) the number of conjugacy classes of subgroups of G not in CD(G). In this paper, we determine the finite groups G such that v(G)=1,2,3.

We show that in the extended modular group PGL(2,Z) there are exactly seven finite subgroups up to conjugacy; three subgroups of size 2, one subgroup each of size 3, 4, and 6, and the trivial subgroup of size 1.

Suppose $C(G)$ denotes the set of all cyclic subgroups of a finite group $G$, and $\mathcal{O}_{2}(G)$ denotes the number of elements of order $2$ in $G$. In [Marius T., Finite groups with a certain number of cyclic subgroups. The American…

In this paper, we provide new criteria for the solvability and supersolvability of a finite group based on its number of cyclic subgroups. A finite group G is called n-cyclic if it contains n cyclic subgroups. This paper also partially…

In this note we study the finite groups whose subgroup lattices are dismantlable.