@article {3131510,
	title = {Permutation groups with restricted stabilizers},
	journal = {Journal of Algebra},
	volume = {607},
	year = {2022},
	note = {Accession Number: S0021869321004142; Author: Burness, Timothy C. (a); Author: Shalev, Aner (b); Affiliation: School of Mathematics, University of Bristol, Bristol BS8 1UG, UK; Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel; AS acknowledges the support of ISF grant 686/17 and the Vinik Chair of Mathematics which he holds. Both authors thank Joanna Fawcett and Michael Giudici for helpful comments on twisted wreath products. They also thank an anonymous referee for many insightful comments, corrections and suggestions on an earlier version of this paper.; Keyword: Primitive groups; Keyword: Restricted stabilizers; Keyword: Base sizes; Number of Pages: 26; Language: English;},
	month = {2022/10/01/Octob},
	pages = {160 - 185},
	publisher = {Elsevier Inc.},
	abstract = {Fix a positive integer d and let Γd be the class of finite groups without sections isomorphic to the alternating group Ad. The groups in Γd were studied by Babai, Cameron and P{\'a}lfy in the 1980s and they determined bounds on the order of a primitive permutation group with this property, which have found a wide range of applications. Subsequently, results on the base sizes of such groups were also obtained. In this paper we replace the structural conditions on the group by restrictions on its point stabilizers, and we obtain similar, and sometimes stronger conclusions. For example, we prove that there is a linear function f such that the base size of any finite primitive group with point stabilizers in Γd is at most f(d). This generalizes a recent result of the first author on primitive groups with solvable point stabilizers. For non-affine primitive groups we obtain stronger results, assuming only that stabilizers of c points lie in Γd. We also show that if G is any permutation group of degree n whose c-point stabilizers lie in Γd, then |G|⩽((1+oc(1))d/e)n-1. This asymptotically extends and improves a dn-1 upper bound on |G| obtained by Babai, Cameron and P{\'a}lfy assuming G∈Γd.},
	keywords = {Base sizes, Primitive groups, Restricted stabilizers},
	isbn = {0021-8693},
	url = {https://search.ebscohost.com/login.aspx?direct=true\&AuthType=ip,shib\&db=edselp\&AN=S0021869321004142\&site=eds-live\&scope=site\&custid=s5122861\&authtype=shib},
	author = {Burness, Timothy C. and Aner Shalev}
}
