Primary graded groups with systems of complemented subgroups.
This paper investigates the productivity of the Zariski topology of a group . If is a family of groups, and is their direct product, we prove that . This inclusion can be proper in general, and we describe the doubletons of abelian groups, for which the converse inclusion holds as well, i.e., . If is the identity element of a group , we also describe the class of groups such that is an elementary algebraic subset of for every group . We show among others, that is stable...
In this paper we deal with the notions of projectability, spliting property and Dedekind completeness of lattice ordered groups, and with the relations between these notions.
We describe the finite groups satisfying one of the following conditions: all maximal subgroups permute with all subnormal subgroups, (2) all maximal subgroups and all Sylow -subgroups for permute with all subnormal subgroups.
This article is dedicated to some criteria of generalized nilpotency involving pronormality and abnormality. Also new results on groups, in which abnormality is a transitive relation, have been obtained.
Two virtual link diagrams are homotopic if one may be transformed into the other by a sequence of virtual Reidemeister moves, classical Reidemeister moves, and self crossing changes. We recall the pure virtual braid group. We then describe the set of pure virtual braids that are homotopic to the identity braid.