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pro vyhledávání: '"Camina, Rachel"'
Many results have been established that show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper is to show several results about solvability concerning the case in whi
Externí odkaz:
http://arxiv.org/abs/2402.06703
Given a discrete (resp. profinite) group $G$, we define $NCC(G)$ to be the smallest number of cyclic (resp. procyclic) subgroups of $G$ whose conjugates cover $G$. In this paper we determine all residually finite discrete groups with finite NCC and g
Externí odkaz:
http://arxiv.org/abs/2210.15746
The Amit conjecture about word maps on finite nilpotent groups has been shown to hold for certain classes of groups. The generalised Amit conjecture says that the probability of an element occurring in the image of a word map on a finite nilpotent gr
Externí odkaz:
http://arxiv.org/abs/2201.04860
Autor:
Camina, Alan R., Camina, Rachel D.
We continue the investigation, that began in [3] and [4], into finite groups whose set of nontrivial conjugacy class sizes form an arithmetic progression. Let $G$ be a finite group and denote the set of conjugacy class sizes of $G$ by ${\rm cs}(G)$.
Externí odkaz:
http://arxiv.org/abs/2009.05355
Let $G$ be a finite group, and let cs$(G)$ be the set of conjugacy class sizes of $G$. Recalling that an element $g$ of $G$ is called a \emph{vanishing element} if there exists an irreducible character of $G$ taking the value $0$ on $g$, we consider
Externí odkaz:
http://arxiv.org/abs/2005.03757
Let $w$ be a word in $k$ variables. For a finite nilpotent group $G$, a conjecture of Amit states that $N_w(1) \ge |G|^{k-1}$, where $N_w(1)$ is the number of $k$-tuples $(g_1,...,g_k)\in G^{(k)}$ such that $w(g_1,...,g_k)=1$. Currently, this conject
Externí odkaz:
http://arxiv.org/abs/2005.03634
Let $G$ be a finite group. An element $g$ of $G$ is called a vanishing element if there exists an irreducible character $\chi$ of $G$ such that $\chi(g) = 0$; in this case, we say that the conjugacy class of $g$ is a vanishing conjugacy class. In thi
Externí odkaz:
http://arxiv.org/abs/1706.05611
Given a finite group $G$, denote by $\Gamma(G)$ the simple undirected graph whose vertices are the distinct sizes of noncentral conjugacy classes of $G$, and set two vertices of $\Gamma(G)$ to be adjacent if and only if they are not coprime numbers.
Externí odkaz:
http://arxiv.org/abs/1306.1558
Autor:
Camina, Alan, Camina, Rachel
This is a survey of way that the sizes of conjugacy classes influence the structure of finite groups
Comment: This is a new version. We would like to thanks those who made comments.
Comment: This is a new version. We would like to thanks those who made comments.
Externí odkaz:
http://arxiv.org/abs/1002.3960