Prime divisors and the number of conjugacy classes of finite groups
نویسندگان
چکیده
Abstract We prove that there exists a universal constant D such if p is prime divisor of the index Fitting subgroup finite group G , then number conjugacy classes at least $Dp/\log_2p$ . conjecture we can take $D=1$ and for solvable groups, $D=1/3$
منابع مشابه
COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS
Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...
متن کاملON THE NUMBER OF CONJUGACY CLASSES OF FINITE p-GROUPS
Denote k(G) the number of conjugacy classes of a group G. Some inequalities are deduced by arithmetic means for k(G), where G is a p-group. As an application, k(G) is calculated for special cases of p-groups. A method of estimating k(G) for some finite groups, others then p-groups is also presented.
متن کاملOn the number of conjugacy classes of finite nilpotent groups
We establish the first super-logarithmic lower bound for the number of conjugacy classes of a finite nilpotent group. In particular, for any constant c there are only finitely many finite p-groups of order pm with at most c ·m conjugacy classes. This answers a question of L. Pyber.
متن کاملOn the Regular Power Graph on the Conjugacy Classes of Finite Groups
emph{The (undirected) power graph on the conjugacy classes} $mathcal{P_C}(G)$ of a group $G$ is a simple graph in which the vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent in $mathcal{P_C}(G)$ if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are $k$-regular for $k=5,6$.
متن کاملFINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES
Let G be a finite group and Z(G) be the center of G. For a subset A of G, we define kG(A), the number of conjugacy classes of G that intersect A non-trivially. In this paper, we verify the structure of all finite groups G which satisfy the property kG(G-Z(G))=5, and classify them.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical proceedings of the Cambridge Philosophical Society
سال: 2023
ISSN: ['0305-0041', '1469-8064']
DOI: https://doi.org/10.1017/s030500412300035x