Product Action Taken Relationship Delay Duration

2020 ◽  
Author(s):  
2006 ◽  
Author(s):  
Steven P. Woods ◽  
Matthew S. Dawson ◽  
Catherine L. Carey ◽  
Erin E. Morgan ◽  
Igor Grant

10.37236/4831 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Ashish Mishra ◽  
Murali K. Srinivasan

Let $G$ be a finite group acting on the finite set $X$ such that the corresponding (complex) permutation representation is multiplicity free. There is a natural rank and order preserving action of the wreath product $G\sim S_n$ on the generalized Boolean algebra $B_X(n)$. We explicitly block diagonalize the commutant of this action.


2001 ◽  
Vol 33 (6) ◽  
pp. 653-661 ◽  
Author(s):  
CAI HENG LI ◽  
CHERYL E. PRAEGER

A construction is given of an infinite family of finite self-complementary, vertex-transitive graphs which are not Cayley graphs. To the authors' knowledge, these are the first known examples of such graphs. The nature of the construction was suggested by a general study of the structure of self-complementary, vertex-transitive graphs. It involves the product action of a wreath product of permutation groups.


2012 ◽  
Vol 92 (1) ◽  
pp. 127-136 ◽  
Author(s):  
CHERYL E. PRAEGER ◽  
CSABA SCHNEIDER

AbstractWe consider the wreath product of two permutation groups G≤Sym Γ and H≤Sym Δ as a permutation group acting on the set Π of functions from Δ to Γ. Such groups play an important role in the O’Nan–Scott theory of permutation groups and they also arise as automorphism groups of graph products and codes. Let X be a subgroup of Sym Γ≀Sym Δ. Our main result is that, in a suitable conjugate of X, the subgroup of SymΓ induced by a stabiliser of a coordinate δ∈Δ only depends on the orbit of δ under the induced action of X on Δ. Hence, if X is transitive on Δ, then X can be embedded into the wreath product of the permutation group induced by the stabiliser Xδ on Γ and the permutation group induced by X on Δ. We use this result to describe the case where X is intransitive on Δ and offer an application to error-correcting codes in Hamming graphs.


2017 ◽  
Vol 17 (14) ◽  
pp. 10 ◽  
Author(s):  
Hongsup Shin ◽  
Qijia Zou ◽  
Wei Ji Ma

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Wongsa Laohasiriwong ◽  
Roshan Kumar Mahato ◽  
Rajendra Koju ◽  
Kriangsak Vaeteewootacharn

Tuberculosis (TB) is still a major public health challenge in Nepal and worldwide. Most transmissions occur between the onset of symptoms and the consultation with formal health care centers. This study aimed to determine the duration of delay for the first consultation and its associated factors with unacceptable delay among the new sputum pulmonary tuberculosis cases in the central development region of Nepal. An analytical cross-sectional study was conducted in the central development region of Nepal between January and May 2015. New pulmonary sputum positive tuberculosis patients were interviewed by using a structured questionnaire and their medical records were reviewed. Among a total of 374 patients, the magnitude of patient delay was 53.21% (95% CI: 48.12–58.28%) with a median delay of 32 days and an interquartile range of 11–70 days. The factors associated with unacceptable patient delay (duration ≥ 30 days) were residence in the rural area (adj. OR = 3.10, 95% CI: 1.10–8.72;pvalue = 0.032) and DOTS center located more than 5 km away from their residences (adj. OR = 5.53, 95% CI: 2.18–13.99;pvalue < 0.001). Unemployed patients were more likely to have patient delay (adj. OR = 7.79, 95% CI: 1.64–37.00;pvalue = 0.010) when controlled for other variables.


1989 ◽  
Vol 40 (2) ◽  
pp. 255-279 ◽  
Author(s):  
L. G. Kovács

There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding ‘imprimitive wreath decomposition’ concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The result may be heuristically expressed as follows, exploiting the associative nature of the construction. Each finite transitive permutation group may be written, essentially uniquely, as the wreath product of a sequence of wreath-indecomposable groups, amid the two-factor wreath decompositions of the group are precisely those which one obtains by bracketing this many-factor decomposition.If both input groups are nontrivial, the output above is always imprimitive. A similar construction gives a primitive output, called the wreath product in product action, provided the first input group is primitive and not regular. The second subject of the paper is the ‘product action wreath decomposition’ concept dual to this. An analogue of the result stated above is established for primitive groups with nonabelian socle.Given a primitive subgroup G with non-regular socle in some symmetric group S, how many subgroups W of S which contain G and have the same socle, are wreath products in product action? The third part of the paper outlines an algorithm which reduces this count to questions about permutation groups whose degrees are very much smaller than that of G.


Sign in / Sign up

Export Citation Format

Share Document