Quasirandom Groups

2008 ◽  
Vol 17 (3) ◽  
pp. 363-387 ◽  
Author(s):  
W. T. GOWERS
Keyword(s):  
Finite Group ◽  
Sufficient Condition ◽  
Large Product ◽  
Simple Sufficient Condition ◽  
Free Subset

Babai and Sós have asked whether there exists a constant c > 0 such that every finite group G has a product-free subset of size at least c|G|: that is, a subset X that does not contain three elements x, y and z with xy = z. In this paper we show that the answer is no. Moreover, we give a simple sufficient condition for a group not to have any large product-free subset.

Some results on the classification of expansive automorphisms of compact abelian groups

1996 ◽  
Vol 16 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Fabio Fagnani
Keyword(s):  
Finite Group ◽  
Topological Entropy ◽  
Abelian Groups ◽  
Topological Classification ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compact Abelian Groups ◽  
A Finite Group ◽  
Necessary And Sufficient

AbstractIn this paper we study expansive automorphisms of compact 0-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements isp2for a primep. This yields a classification of the transitive expansive automorphisms with topological entropy logp2. Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.

scholarly journals On extension of characters from normal subgroups

1984 ◽  
Vol 27 (1) ◽  
pp. 7-9 ◽  
Author(s):  
G. Karpilovsky
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Sufficient Condition ◽  
Normal Subgroups ◽  
Complex Character ◽  
A Finite Group

In what follows, character means irreducible complex character.Let G be a finite group and let % be a character of a normal subgroup N. If χ extends to a character of G then χ is stabilised by G, but the converse is false. The aim of this paper is to prove the following theorem which gives a sufficient condition for χ to be extended to a character of G.

Some Characterizations about the Structure of Finite Groups

2012 ◽  
Vol 19 (03) ◽  
pp. 563-568
Author(s):  
Lili Wang ◽  
Guiyun Chen
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sufficient Condition ◽  
A Finite Group

A subgroup H of a finite group G is called an ℋ-subgroup of G if NG(H) ∩ Hg ≤ H for all g ∈ G. The set of all ℋ-subgroups of a finite group G is denoted by ℋ(G). In this paper, a sufficient condition about p-nilpotency is given and some new results for a finite group G to be p-nilpotent or supersolvable are obtained based on the assumption that some subgroups belong to ℋ(G).

scholarly journals A finite model-theoretical proof of a property of bounded query classes within PH

2004 ◽  
Vol 69 (4) ◽  
pp. 1105-1116 ◽  
Author(s):  
Leszek Aleksander Kołodziejczyk
Keyword(s):  
Normal Form ◽  
Model Theory ◽  
Finite Model ◽  
Sufficient Condition ◽  
Finite Model Theory ◽  
Finite Models ◽  
Constructible Function ◽  
Simple Sufficient Condition

Abstract.We use finite model theory (in particular, the method of FM-truth definitions, introduced in [MM01] and developed in [K04], and a normal form result akin to those of [Ste93] and [G97]) to prove:Let m ≥ 2. Then:(A) If there exists k such that NP⊆ Σm TIME(nk)∩ Πm TIME(nk), then for every r there exists kr such that :(B) If there exists a superpolynomial time-constructible function f such that NTIME(f), then additionally .This strengthens a result by Mocas [M96] that for any r, .In addition, we use FM-truth definitions to give a simple sufficient condition for the arity hierarchy to be strict over finite models.

A simple sufficient condition for triviality of obstructions in the orbifold construction for subfactors

2017 ◽  
Vol 121 (1) ◽  
pp. 101
Author(s):  
Toshihiko Masuda
Keyword(s):  
Sufficient Condition ◽  
Principal Graph ◽  
Simple Sufficient Condition ◽  
Orbifold Construction

We present a simple sufficient condition for triviality of obstructions in the orbifold construction. As an application, we can show the existence of subfactors with principal graph $D_{2n}$ without full use of Ocneanu's paragroup theory.

scholarly journals A Restless Bandit Model for Resource Allocation, Competition, and Reservation

2021 ◽  
Author(s):  
Jing Fu ◽  
Bill Moran ◽  
Peter G. Taylor
Keyword(s):  
Resource Allocation ◽  
Numerical Experiments ◽  
Asymptotic Optimality ◽  
Sufficient Condition ◽  
Limited Capacity ◽  
Index Policy ◽  
Asymptotically Optimal ◽  
Restless Bandit ◽  
Simple Sufficient Condition ◽  
Resource Capacity

In “A Restless Bandit Model for Resource Allocation, Competition and Reservation,” J. Fu, B. Moran, and P. G. Taylor study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. This problem is modeled as a set of heterogeneous restless multi-armed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle’s idea of relaxing the constraints and Weber and Weiss’s proof of asymptotic optimality, the authors propose an index policy and establish conditions for it to be asymptotically optimal in a regime where both arrival rates and capacities increase. In particular, they provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. Via numerical experiments, they demonstrate the effectiveness of these results even in the pre-limit case.

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