منابع مشابه
On the Conjugacy of Orthogonal Groups
In much of the mathematical literature, there is talk about the (note the definite article) orthogonal group O(n, F I ) of degree n ∈ N I over a field F I . This is extremely misleading, because, given a linear space T of dimension n, one can consider the orthogonal group of any non-degenerate quadratic form Q on T . In Chapter 6 of the book Basic Algebra I [J], Jacobson denotes this orthogonal...
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We give a unified solution the conjugacy problem in Thompson’s groups F , V , and T using strand diagrams, a modification of tree diagrams. We then analyze the complexity of the resulting algorithms. Thompson’s group F is the group of all piecewise-linear homeomorphisms of the unit interval satisfying the following conditions: 1. Every slope is a power of two, and 2. Every breakpoint has dyadic...
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Let G be a reductive algebraic group and H be a connected semisimple subgroup of G. The dimension data consists of the collection { dimV H } with V H denoting the space of points in V fixed by H , and where (ρ, V ) runs through all representations of G. One may ask if the dimension data determine H up to conjugacy or at least isomorphism. In other words, If H and H ′ have the same dimension dat...
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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 $k=5,6$.
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...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2019
ISSN: 1435-4446,1433-5883
DOI: 10.1515/jgth-2018-0137