On Pyber's base size conjecture

Tim C Burness, A Seress

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)
31 Downloads (Pure)

Abstract

Let G be a permutation group on a finite set S. A subset of S is a base for G if its pointwise stabilizer in G is trivial. The base size of G, denoted b(G), is the smallest size of a base. A well known conjecture of Pyber from the early 1990s asserts that there exists an absolute constant c such that b(G) is at most c.log |G| / log n for any primitive permutation group G of degree n. Some special cases have been verified in recent years, including the almost simple and diagonal cases. In this paper, we prove Pyber's conjecture for all non-affine primitive groups.
Original languageEnglish
Pages (from-to)5633-5651
Number of pages19
JournalTransactions of the American Mathematical Society
Volume367
DOIs
Publication statusPublished - 2015

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