In this paper we discuss the splitting or decomposing of finitely generated groups into free products, free products with amalgamation or HNN extensions and we discuss the JSJ decomposition of finitely presented groups.

Although neural networks have been widely applied to medical problems in recent years, their applicability has been limited for a variety of reasons. One of these barriers has been the inability to discriminate rare classes of solutions (i.e., the identification of categories that are infrequent). In this article, I demonstrate that a system of hierarchical neural networks (HNN) can overcome th...

a subgroup h of a group g is called inert if‎, ‎for each $gin g$‎, ‎the index of $hcap h^g$ in $h$ is finite‎. ‎we give a classification ‎of soluble-by-finite groups $g$ in which subnormal subgroups are inert in the cases where $g$ has no nontrivial torsion normal subgroups or $g$‎ ‎is finitely generated‎.