The conjugacy problem for finite graph products
نویسندگان
چکیده
منابع مشابه
The Conjugacy Problem for Finite Graph Products
A finite graph product is the fundamental group of a finite graph of groups. Finite graph products with finite cyclic edge groups are shown to inherit a solvable conjugacy problem from their vertex groups under certain conditions, of which the most important is that all the edge group generators in each vertex group are powers of a common central element.
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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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A graph product is the fundamental group of a graph of groups Amongst the simplest examples are HNN groups and free products with amalgamation. The conjugacy problem is solvable for recursively presented graph products with cyclic edge groups over finite graphs if the vertex groups have solvable conjugacy problem and the sets of cyclic generators in them are semicritical. For graph products ove...
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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...
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 $k=5,6$.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1989
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1989-0962244-5