FINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES
نویسندگان
چکیده مقاله:
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.
منابع مشابه
finite 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 $k_g(a)$, the number of conjugacy classes of $g$ which intersect $a$ non-trivially. in this paper, we verify the structure of all finite groups $g$ which satisfy the property $k_g(g-z(g))=5$ and classify them.
متن کاملNilpotent groups with three conjugacy classes of non-normal subgroups
Let $G$ be a finite group and $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$. In this paper, all nilpotent groups $G$ with $nu(G)=3$ are classified.
متن کاملCOMPUTING 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 کاملCONJUGACY CLASSES IN FINITE p-GROUPS
Of course, in that problem we have to take into account that the class sizes impose restrictions on the group structure. E.g. if the sizes are {1, p}, then the nilpotency class has to be 2. More precisely: the class sizes of a p-group G are {1, p} iff |G′| = p (Knoche; see also Theorem 3 below). But we can ask, e.g., if, given any set S ≠ {1, p} of p-powers, does there exist a group of class 3 ...
متن کاملFinite Groups Have More Conjugacy Classes
We prove that for every > 0 there exists a δ > 0 so that every group of order n ≥ 3 has at least δ log2 n/(log2 log2 n) 3+ conjugacy classes. This sharpens earlier results of Pyber and Keller. Bertram speculates whether it is true that every finite group of order n has more than log3 n conjugacy classes. We answer Bertram’s question in the affirmative for groups with a trivial solvable radical.
متن کاملnilpotent groups with three conjugacy classes of non-normal subgroups
let $g$ be a finite group and $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$. in this paper, all nilpotent groups $g$ with $nu(g)=3$ are classified.
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 4 شماره 2
صفحات 85- 95
تاریخ انتشار 2017-01-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
کلمات کلیدی
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023