system of imprimitivity
Recently Published Documents


TOTAL DOCUMENTS

5
(FIVE YEARS 0)

H-INDEX

1
(FIVE YEARS 0)

2015 ◽  
Vol 93 (1) ◽  
pp. 13-18
Author(s):  
M. REZA SALARIAN

Let $G$ be a finite group and ${\rm\Gamma}$ a $G$-symmetric graph. Suppose that $G$ is imprimitive on $V({\rm\Gamma})$ with $B$ a block of imprimitivity and ${\mathcal{B}}:=\{B^{g};g\in G\}$ a system of imprimitivity of $G$ on $V({\rm\Gamma})$. Define ${\rm\Gamma}_{{\mathcal{B}}}$ to be the graph with vertex set ${\mathcal{B}}$ such that two blocks $B,C\in {\mathcal{B}}$ are adjacent if and only if there exists at least one edge of ${\rm\Gamma}$ joining a vertex in $B$ and a vertex in $C$. Xu and Zhou [‘Symmetric graphs with 2-arc-transitive quotients’, J. Aust. Math. Soc. 96 (2014), 275–288] obtained necessary conditions under which the graph ${\rm\Gamma}_{{\mathcal{B}}}$ is 2-arc-transitive. In this paper, we completely settle one of the cases defined by certain parameters connected to ${\rm\Gamma}$ and ${\mathcal{B}}$ and show that there is a unique graph corresponding to this case.


2014 ◽  
Vol 14 (3&4) ◽  
pp. 339-360
Author(s):  
D.M. Appleby ◽  
Ingemar Bengtsson ◽  
Stephen Brierley ◽  
Asa Ericsson ◽  
Markus Grassl ◽  
...  

It is known that if the dimension is a perfect square the Clifford group can be represented by monomial matrices. Another way of expressing this result is to say that when the dimension is a perfect square the standard representation of the Clifford group has a system of imprimitivity consisting of one dimensional subspaces. We generalize this result to the case of an arbitrary dimension. Let k be the square-free part of the dimension. Then we show that the standard representation of the Clifford group has a system of imprimitivity consisting of $k$-dimensional subspaces. To illustrate the use of this result we apply it to the calculation of SIC-POVMs (symmetric informationally complete positive operator valued measures), constructing exact solutions in dimensions 8 (hand-calculation) as well as 12 and 28 (machine-calculation).


2011 ◽  
Vol 14 ◽  
pp. 87-98 ◽  
Author(s):  
Tobias Rossmann

AbstractWe describe a practical algorithm for primitivity testing of finite nilpotent linear groups over various fields of characteristic zero, including number fields and rational function fields over number fields. For an imprimitive group, a system of imprimitivity can be constructed. An implementation of the algorithm in Magma is publicly available.


Author(s):  
J. V. Corbett

AbstractA relation between positive commutators and absolutely continuous spectrum is obtained. If i[Y, Z] = 2Y holds on a core for Z and if Y is positive then we have a system of imprimitivity for the group on , from which it follows that Y has no singular continuous spectrum.


Sign in / Sign up

Export Citation Format

Share Document