Conjugacy expansiveness in finite groups
نویسندگان
چکیده
منابع مشابه
character expansiveness in finite groups
we say that a finite group $g$ is conjugacy expansive if for anynormal subset $s$ and any conjugacy class $c$ of $g$ the normalset $sc$ consists of at least as many conjugacy classes of $g$ as$s$ does. halasi, mar'oti, sidki, bezerra have shown that a groupis conjugacy expansive if and only if it is a direct product ofconjugacy expansive simple or abelian groups.by considering a character analo...
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 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 کاملConjugacy of Finite Subsets in Hyperbolic Groups
There is a quadratic-time algorithm that determines conjugacy between finite subsets in any torsion-free hyperbolic group. Moreover, in any k-generator, δ-hyperbolic group Γ, if two finite subsets A and B are conjugate, then x−1Ax = B for some x ∈ Γ with ‖x‖ less than a linear function of max{‖γ‖ : γ ∈ A∪B}. (The coefficients of this linear function depend only on k and δ.) These results have i...
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: Journal of Group Theory
سال: 2012
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt-2012-0004