Invariable generation and the chebotarev invariant of a finite group

A subset S of a finite group G invariably generates G if G = <hsg(s) j s 2 Si > for each choice of g(s) 2 G; s 2 S. We give a tight upper bound on the minimal size of an invariable generating set for an arbitrary finite group G. In response to a question in [KZ] we also bound the size of a randomly chosen set of elements of G that is likely to generate G invariably. Along the way we prove that every finite simple group is invariably generated by two elements.Comment: Improved versio

Missing children: risks, repeats and responses

Investigating reports of missing children is a major source of demand for the police in the UK. Repeat disappearances are common, can indicate underlying vulnerabilities and have been linked with various forms of exploitation and abuse. Inspired by research on repeat victimisation, this paper examines the prevalence and temporal patterns of repeat missing episodes by children, as well as the characteristics of those involved. Using data on all missing children incidents recorded by one UK police service in 2015 (n = 3,352), we find that: (a) 75% of missing incidents involving children were repeats, i.e. attributed to children who had already been reported missing in 2015; (b) a small proportion of repeatedly missing children (n = 59; 4%) accounted for almost a third of all missing children incidents (n = 952, 28%); (c) over half of all first repeat disappearances occurred within four weeks of an initial police recorded missing episode; and (d) children recorded as missing ten times or more over the one year study period were significantly more likely than those recorded missing once to be teenagers, in the care system or to have drug and/or alcohol dependencies. We conclude by discussing the implications of our findings for future research and the prevention of repeat disappearances by children

Effects of Union Organization on Strike Incidence in EU Companies

The author reinvestigates the relationship between the organizational power of trade unions and strikes based on data from the European Company Survey 2009 (ECS-2009) and the Institutional Characteristics of Trade Unions, Wage Setting, State Intervention and Social Pacts (ICTWSS) database, which include more than 5,000 firms across all 27 European Union (EU) member states. He shows that the incidence of strikes is higher in companies for which workplace union membership is high, the number of workplace unions is high, and unions dominate establishment-level works councils. These factors interact to affect strike incidence. In addition, the company-level effects of union organization on strike incidence vary across countries. These country differences can partially be explained by differences in national trade union systems, such as decentralization and membership density