منابع مشابه
CONJUGACY 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 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 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 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 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.
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2005
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-005-1398-7