Zobrazeno 1 - 10
of 57
pro vyhledávání: '"MONETTA, CARMINE"'
Autor:
Lewis, Mark L., Monetta, Carmine
This article investigates neighborhoods' sizes in the enhanced power graph (as known as the cyclic graph) associated with a finite group. In particular, we characterize finite $p$-groups with the smallest maximum size for neighborhoods of nontrivial
Externí odkaz:
http://arxiv.org/abs/2408.16545
The study of verbal subgroups within a group is well-known for being an effective tool to obtain structural information about a group. Therefore, conditions that allow the classification of words in a free group are of paramount importance. One of th
Externí odkaz:
http://arxiv.org/abs/2404.06308
There are many group-based cryptosystems in which the security relies on the difficulty of solving Conjugacy Search Problem (CSP) and Simultaneous Conjugacy Search Problem (SCSP) in their underlying platform groups. In this paper we give a cryptanaly
Externí odkaz:
http://arxiv.org/abs/2309.13928
Autor:
Hadjievangelou, Anastasia, Longobardi, Patrizia, Maj, Mercede, Monetta, Carmine, O'Brien, E. A., Traustason, Gunnar
We survey left 3-Engel elements in groups.
Externí odkaz:
http://arxiv.org/abs/2306.06592
Let $\Gamma_G$ denote a graph associated with a group $G$. A compelling question about finite groups asks whether or not a finite group $H$ must be nilpotent provided $\Gamma_H$ is isomorphic to $\Gamma_G$ for a finite nilpotent group $G$. In the pre
Externí odkaz:
http://arxiv.org/abs/2303.01093
Autor:
Grazian, Valentina, Monetta, Carmine
In this work we discuss whether the non-commuting graph of a finite group can determine its nilpotency. More precisely, Abdollahi, Akbari and Maimani conjectured that if $G$ and $H$ are finite groups with isomorphic non-commuting graphs and $G$ is ni
Externí odkaz:
http://arxiv.org/abs/2302.01770
On the structure of finite groups determined by the arithmetic and geometric means of element orders
In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions strongly affect the group structure. In particular, for every prime $p$, we
Externí odkaz:
http://arxiv.org/abs/2212.13770
Let $G$ be a finite group of order $n$, and denote by $\rho(G)$ the product of element orders of $G$. The aim of this work is to provide some upper bounds for $\rho(G)$ depending only on $n$ and on its least prime divisor, when $G$ belongs to some cl
Externí odkaz:
http://arxiv.org/abs/2205.12316
The solubility graph $\Gamma_S(G)$ associated with a finite group $G$ is a simple graph whose vertices are the elements of $G$, and there is an edge between two distinct vertices if and only if they generate a soluble subgroup. In this paper, we focu
Externí odkaz:
http://arxiv.org/abs/2202.09563
Let $G$ be a finite group, let $p$ be a prime and let $w$ be a group-word. We say that $G$ satisfies $P(w,p)$ if the prime $p$ divides the order of $xy$ for every $w$-value $x$ in $G$ of $p'$-order and for every non-trivial $w$-value $y$ in $G$ of or
Externí odkaz:
http://arxiv.org/abs/2105.14474