Zobrazeno 1 - 10
of 311
pro vyhledávání: '"Tărnăuceanu, Marius"'
Autor:
Tărnăuceanu, Marius
A group $G$ is said to have dense solitary subgroups if each non-empty open interval in its subgroup lattice $L(G)$ contains a solitary subgroup. In this short note, we find all finite groups satisfying this property.
Comment: Accepted for publi
Comment: Accepted for publi
Externí odkaz:
http://arxiv.org/abs/2412.08782
Autor:
Tărnăuceanu, Marius
Publikováno v:
Bull. Korean Math. Soc., vol. 57 (2020), no. 6, pp. 1475-1479
Let $G$ be a finite group and $\sigma_1(G)=\frac{1}{|G|}\sum_{H\leq G}\,|H|$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of $G$, we prove that if $\sigma_1(G)<\frac{117}{20}\,$, then $G$ is solvable.
Externí odkaz:
http://arxiv.org/abs/2409.13077
Autor:
Tărnăuceanu, Marius
In this short note, we describe finite groups all of whose non-trivial cyclic subgroups have the same Chermak-Delgado measure.
Comment: accepted for publication in Facta Univ., Series Math. Inform
Comment: accepted for publication in Facta Univ., Series Math. Inform
Externí odkaz:
http://arxiv.org/abs/2408.16781
In this article we introduce the concept of almost $\mathcal{P}$-numbers. We survey the existing results in literature for almost cyclic numbers and give characterizations for almost abelian and almost nilpotent numbers proving these two are equivale
Externí odkaz:
http://arxiv.org/abs/2408.08427
Autor:
Tărnăuceanu, Marius
In this note, we prove that for every integer $d\geq 2$ which is not a prime power, there exists a finite solvable group $G$ such that $d\mid |G|$, $\pi(G)=\pi(d)$ and $G$ has no subgroup of order $d$. We also introduce the CLT-degree of a finite gro
Externí odkaz:
http://arxiv.org/abs/2403.05774
Autor:
Fasolă, Georgiana, Tărnăuceanu, Marius
Given a construction $f$ on groups, we say that a group $G$ is \textit{$f$-realisable} if there is a group $H$ such that $G\cong f(H)$, and \textit{completely $f$-realisable} if there is a group $H$ such that $G\cong f(H)$ and every subgroup of $G$ i
Externí odkaz:
http://arxiv.org/abs/2310.12372
In this paper, we introduce a new function computing the harmonic mean of element orders of a finite group. We present a series of properties for this function, and then we study groups for which the value of the function is an integer.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2310.00181
Autor:
Fasolă, Georgiana, Tărnăuceanu, Marius
Given a construction $f$ on groups, we say that a group $G$ is \textit{$f$-realisable} if there is a group $H$ such that $G\cong f(H)$, and \textit{completely $f$-realisable} if there is a group $H$ such that $G\cong f(H)$ and every subgroup of $G$ i
Externí odkaz:
http://arxiv.org/abs/2303.15636