CONJUGACY CLASSES OF AUTOMORPHISMS p-GROUPS
نویسندگان
چکیده
منابع مشابه
Groups with Finitely Many Conjugacy Classes and Their Automorphisms
We combine classical methods of combinatorial group theory with the theory of small cancellations over relatively hyperbolic groups to construct finitely generated torsion-free groups that have only finitely many classes of conjugate elements. Moreover, we present several results concerning embeddings into such groups. As another application of these techniques, we prove that every countable gr...
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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 ...
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Let K be an algebraically closed field of characteristic 0 and let K and P denote respectively the affine and projective n-spaces over K. The Cremona group, which is the group of birational maps of these two spaces,Bir(K) = Bir(P), has been studied a lot, especially in dimension 2 and 3, see for example [Hud] and [AlC]. Its subgroup of biregular morphisms (or automorphisms) of K, called the aff...
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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.
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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...
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ژورنال
عنوان ژورنال: Bulletin of the Korean Mathematical Society
سال: 2011
ISSN: 1015-8634
DOI: 10.4134/bkms.2011.48.4.847