In this paper, the structures of dual Lie bialgebras of twisted Schrödinger-Virasoro type are investigated. By studying the maximal good subspaces, we determine the dual Lie coalgebras of the twisted Schrödinger-Virasoro algebras. Then based on this, we construct the dual Lie bialgebra structures of this type. As by-products, four new infinite dimensional Lie algebras are obtained. [ABSTRACT FROM AUTHOR]
In this paper, we study the cover-avoid property of 픉-injectors on chief factors of a group G for a Fitting class 픉 in some universe 픘 with partial solubility. [ABSTRACT FROM AUTHOR]
Let Θ be a collection of formations. A formation 픉 ∈ Θ is called an ℌΘ-critical formation or a minimal non-ℌ Θ-formation if 픉 ⊈ ℌ but the class ℌ of groups contains each proper Θ-subformation of 픉. In this paper we study ℌΘ-critical formations, where Θ is the class of all τ-closed ω-local formations. [ABSTRACT FROM AUTHOR]