Duyan, H. and Halasi, Zoltán and Maróti, Attila (2018) A proof of Pyber's base size conjecture. ADVANCES IN MATHEMATICS, 331. pp. 720747. ISSN 00018708

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Abstract
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 logG/logn≤b(G)<45(logG/logn)+c. This finishes the proof of Pyber's base size conjecture. The main part of our paper is to prove this statement for affine permutation groups G=V⋊H where H≤GL(V) is an imprimitive linear group. An ingredient of the proof is that for the distinguishing number d(G) (in the sense of Albertson and Collins) of a transitive permutation group G of degree n>1 we have the estimates Gn<d(G)≤48Gn. © 2018 Elsevier Inc.
Item Type:  Article 

Uncontrolled Keywords:  SET; FINITE; ORDERS; Permutation group; minimal base size; LINEARGROUPS; REGULAR ORBITS; PRIMITIVE PERMUTATIONGROUPS; Linear group; Distinguishing number; 
Subjects:  Q Science / természettudomány > QA Mathematics / matematika 
SWORD Depositor:  MTMT SWORD 
Depositing User:  MTMT SWORD 
Date Deposited:  12 Jan 2019 18:06 
Last Modified:  12 Jan 2019 18:06 
URI:  http://real.mtak.hu/id/eprint/89799 
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