175 research outputs found
Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties
We give a new proof that a finitely generated congruence-distributive variety has finitely determined syntactic congruences (or, equivalently, term finite principal congruences), and show that the same does not hold for finitely generated congruence-permutable varieties, even under the additional assumption that the variety is residually very finite
A proof of Pyber's base size conjecture
Building on earlier papers of several authors, we establish that there exists a universal constant c>0 such that the minimal base size b(G) of a primitive permutation group G of degree n satisfies log|G|/logn≤b(G)1 we have the estimates |G|
Congruence modularity implies cyclic terms for finite algebras
An n-ary operation f : A(n) -> A is called cyclic if it is idempotent and f(a(1), a(2), a(3), ... , a(n)) = f(a(2), a(3), ... , a(n), a(1)) for every a(1), ... , a(n) is an element of A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than vertical bar A vertical bar
A note on the probability of generating alternating or symmetric groups
We improve on recent estimates for the probability of generating the
alternating and symmetric groups and . In
particular we find the sharp lower bound, if the probability is given by a
quadratic in . This leads to improved bounds on the largest number
such that a direct product of copies
of can be generated by two elements
Conjugacy classes of -elements and nilpotent/abelian Hall -subgroups
Let be a finite group and be a set of primes. We study finite
groups with a large number of conjugacy classes of -elements. In
particular, we obtain precise lower bounds for this number in terms of the
-part of the order of to ensure the existence of a nilpotent or
abelian Hall -subgroup in .Comment: 18 page
An improved diameter bound for finite simple groups of Lie type
© 2019 London Mathematical Society For a finite group (Formula presented.), let (Formula presented.) denote the maximum diameter of a connected Cayley graph of (Formula presented.). A well-known conjecture of Babai states that (Formula presented.) is bounded by (Formula presented.) in case (Formula presented.) is a non-abelian finite simple group. Let (Formula presented.) be a finite simple group of Lie type of Lie rank (Formula presented.) over the field (Formula presented.). Babai's conjecture has been verified in case (Formula presented.) is bounded, but it is wide open in case (Formula presented.) is unbounded. Recently, Biswas and Yang proved that (Formula presented.) is bounded by (Formula presented.). We show that in fact (Formula presented.) holds. Note that our bound is significantly smaller than the order of (Formula presented.) for (Formula presented.) large, even if (Formula presented.) is large. As an application, we show that more generally (Formula presented.) holds for any subgroup (Formula presented.) of (Formula presented.), where (Formula presented.) is a vector space of dimension (Formula presented.) defined over the field (Formula presented.)
inTrack: High Precision Tracking of Mobile Sensor Nodes
Radio-interferometric ranging is a novel technique that allows
for fine-grained node localization in networks of inexpensive COTS
nodes. In this paper, we show that the approach can also be applied
to precision tracking of mobile sensor nodes. We introduce inTrack, a
cooperative tracking system based on radio-interferometry that features
high accuracy, long range and low-power operation. The system utilizes
a set of nodes placed at known locations to track a mobile sensor. We
analyze how target speed and measurement errors affect the accuracy of
the computed locations. To demonstrate the feasibility of our approach,
we describe our prototype implementation using Berkeley motes. We
evaluate the system using data from both simulations and field tests
A rolling stock circulation model for combining and splitting of passenger trains.
This paper addresses the railway rolling stock circulation problem. Given the departure and arrival times as well as the expected numbers of passengers, we have to assign the rolling stock to the timetable services. We consider several objective criteria that are related to operational costs, service quality and reliability of the railway system. Our model is an extension of an existing rolling stock model for routing train units along a number of connected train lines. The extended model can also handle underway combining and splitting of trains. We illustrate our model by computational experiments based on instances of NS Reizigers, the main Dutch operator of passenger train
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