Journal of Group Theory
Editor-in-Chief: Parker, Christopher W.
Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus
6 Issues per year
IMPACT FACTOR 2017: 0.581
CiteScore 2017: 0.53
SCImago Journal Rank (SJR) 2017: 0.778
Source Normalized Impact per Paper (SNIP) 2017: 0.893
Mathematical Citation Quotient (MCQ) 2017: 0.45
On the single-orbit conjecture for uncoverings-by-bases
Let G be a permutation group acting on a finite set Ω. An uncovering-by-bases (or UBB) for G is a set of bases for G such that any r-subset of Ω is disjoint from at least one base in , where , for d the minimum degree of G. The single-orbit conjecture asserts that for any finite permutation group G, there exists a UBB for G contained in a single orbit of G on its irredundant bases. We prove a case of this conjecture, for when G is k-transitive and has a base of size k + 1. Furthermore, in the more restricted case when G is primitive and has a base of size 2, we show how to construct a UBB of minimum possible size.