Irreducible character degrees and normal subgroups

Let N be a normal subgroup of a finite group G and consider the set cd(G|N) of degrees of irreducible characters of G whose kernels do not contain N. A number of theorems are proved relating the set cd(G|N) to the structure of N. For example, if N is solvable, its derived length is bounded above by a function of |cd(G|N)|. Also, if |cd(G|N)| is at most 2, then N is solvable and its derived length is at most |cd(G|N)|. If G is solvable and |cd(G|N)| = 3, then the derived length of N is at most 3

Real fields and repeated radical extensions

The main result of this paper is that if E is a field extension of finite odd degree over a real field Q, and if E is a repeated radical extension of Q, then every intermediate field is also a repeated radical extension of Q. This paper also contains a number of other results about repeated radical extensions

An unsuccessful resuscitation: The families' and doctors' experiences of the unexpected death of a patient

Background: The objective was to elicit families' experience of the death of a family member at the Elsies River Community Health Centre, their feelings towards the staff involved in the resuscitation and their opinions about how things could be improved. The study also elicited the doctors' experiences of communicating with the families of patients who had died in the emergency unit. Methods: This was a qualitative study, using free attitude interviews for family members and focus group discussions for doctors. Twelve family members whose loved ones had died in the emergency room and 15 doctors who worked in the emergency room were included. Results: Key themes were identified, relating to issues in the pre-resuscitation period, the resuscitation, breaking the bad news, after breaking the bad news and post-event sequelae. In the pre-resuscitation period, there were problems in admitting, identifying and responding to acutely ill patients. During the resuscitation, the families and staff disagreed about witnessing the resuscitation. Breaking the bad news was often difficult for the doctors and hindered by the physical environment. Afterwards, there were mixed feelings about the quality of emotional support, the use of medication and bereavement counselling. All agreed that viewing the body was helpful and funeral arrangements were not a problem. There was no effective follow-up of the families and the doctors also experienced increased stress following unsuccessful resuscitations. Conclusion: The study found that the role of security staff should be clarified and a better triage system established to enable critically ill patients to be seen promptly. Families should be given the option of viewing the resuscitation and always be kept informed of progress. Doctors need better training in communication skills and breaking bad news, which should be done in a private area. Families should also be given the opportunity to view the body. Families should be assisted with contacting the undertaker and a follow-up visit should be organised after the initial shock, when further questions can be asked and abnormal grief reactions identified. Bereavement counselling should be available and community-based resources should be identified in this regard. Debriefing should also be available for staff involved in unsuccessful resuscitations. SA Fam Pract 2004;46(8): 20-2

Asylum seeker’s ‘brain death’ shows failure of care and of democracy

The news that Hamid Kehazaei, a 24-year-old Iranian asylum seeker detained on Manus Island, has been diagnosed as brain dead following his transfer to the Mater Hospital in Brisbane is a tragedy. That it is a tragedy for this young man and his family is unquestionable – but the extent of this tragedy may be much more pervasive than we realise. If the emerging details of his case are correct, Kehazaei developed septicaemia as a complication of cellulitis (skin and soft-tissue infection) arising from a cut in his foot. This, in itself, is disturbing. Severe infection can result in brain death – either from infection of the brain itself (meningitis, encephalitis or brain abscess), or from brain injury due to a lack of oxygen resulting from cardiac arrest (as appears to be the case here), or from reduced blood supply to the brain. Yet it is very uncommon, especially in a young, previously healthy man. Such a case could occur in Australia and has been described in 2012 in young Indigenous adults in Central Australia. Nevertheless, severe sepsis resulting from a foot infection is preventable. And a case like this occurring in an Australian national would raise serious questions about the appropriateness of the antibiotics used and the timeliness of care. Most cases of brain death result from traumatic brain injury, stroke or lack of oxygen to the brain following asphyxia, near-drowning, or prolonged cardiopulmonary resuscitation. What happened to Hamid Kehazaei raises concerns about the adequacy of care provided to him during initial treatment, including wound care and antibiotics, and how soon he was transferred to expert medical care, first to Port Moresby and subsequently to Brisbane. If this young man became ill and had his brain die while seeking asylum in Australia and while in our care, then we must examine the details of his case and ask ourselves not only whether it was preventable but whether our policies and processes actually contributed to his death

X-ray induced persistent photoconductivity in Si-doped Al0.35_{0.35}Ga0.65_{0.65}As

We demonstrate that X-ray irradiation can be used to induce an insulator-metal transition in Si-doped Al$_{0.35}$Ga$_{0.65}$As, a semiconductor with {\it DX} centers. The excitation mechanism of the {\it DX} centers into their shallow donor state was revealed by studying the photoconductance along with fluorescence. The photoconductance as a function of incident X-ray energy exhibits an edge both at the Ga and As K-edge, implying that core-hole excitation of Ga and As are efficient primary steps for the excitation of {\it DX} centers. A high quantum yield ($\gg 1$) suggests that the excitation is indirect and nonlocal, due to secondary electrons, holes, and fluorescence photons.Comment: 3 pages of text, 6 figures. An error in Fig.5 was detected, so we corrected i

Conjugacy classes of p-cycles of type D in alternating groups

We classify the conjugacy classes of p-cycles of type D in alternating groups. This finishes the open cases in arXiv:0812.4628. We also determine all the subracks of those conjugacy classes which are not of type D.Comment: Second paragraph of subsection 2.2 rewritten. 4-th sentence of subsection 2.4 rewritten. More explanations added in Remark 2.4. Lemma 2.5 and Corollary 2.7 added. Appendix removed and put it as Remark 3.1. Remark 3.2 (former 3.1) reorganized. References: [Da], [EGSS], [H], [IS] added, [GPPS] removed. Communications in Algebra (2014