REAL

A proof of Pyber's base size conjecture

Duyan, H. and Halasi, Zoltán and Maróti, Attila (2018) A proof of Pyber's base size conjecture. ADVANCES IN MATHEMATICS, 331. pp. 720-747. ISSN 0001-8708

[img]
Preview
Text
1611.09487v2.pdf

Download (334kB) | Preview

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 log⁡|G|/log⁡n≤b(G)<45(log⁡|G|/log⁡n)+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 |G|n<d(G)≤48|G|n. © 2018 Elsevier Inc.

Item Type: Article
Uncontrolled Keywords: SET; FINITE; ORDERS; Permutation group; minimal base size; LINEAR-GROUPS; REGULAR ORBITS; PRIMITIVE PERMUTATION-GROUPS; 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

Actions (login required)

Edit Item Edit Item