Subnormal structure of non-stable unitary groups over rings

AbstractLet R be a commutative ring with identity in which 2 is invertible. Let H denote a subgroup of the unitary group U(2n,R,Λ) with n≥4. H is normalized by EU(2n,J,ΓJ) for some form ideal (J,ΓJ) of the form ring (R,Λ). The purpose of the paper is to prove that H satisfies a “sandwich” property, i.e. there exists a form ideal (I,ΓI) such that EU(2n,IJ8ΓJ,Γ)⊆H⊆CU(2n,I,ΓI).Furthermore, we give a classification for the subnormal subgroups of the unitary group U(2n,R,Λ), which is an analog for the results existing in the general linear groups; see [L.N. Vaserstein, The subnormal structure of general linear groups over rings, Math. Proc. Cambridge Philos. Soc., 108 (1990) 219–229; N.A. Vavilov, Subnormal structure of general linear group, Math. Proc. Cambridge Philos. Soc. 107 (1990) 103–106; J.S. Wilson, The normal and subnormal structure of general linear groups, Proc. Cambridge Philos. Soc. 71 (1972) 163–177]

Exploring an urban teacher’s use of performance in fostering middle school students’ moral awareness

This study reports on how an urban teacher relied on herself and harnessed performance-based pedagogy in developing her students’ moral awareness over one academic year. Drawing on qualitative analyses of the teacher and students’ reflections, interviews, as well as students’ performance, the study shows that the teacher’s reliance on her own agency in designing a performance-based curriculum counteracted teaching constraints in her workplace. In addition, performance, enacted through engaging students in performing exaggerated bodily activities enabled them to critically reflect upon existing or potential moral issues in their lives and guided their follow-up behaviours. The study concludes the importance of synergising teachers’ self-agency with arts-based education in raising students’ moral awareness, especially in similarly constrained contexts.Keywords: constrained contexts; moral education; performance; pre-tertiary level; teachers’ self-agenc