The direct decompositions of a group $G$ with $G/G’$ finitely generated

Decompositions of finitely generated and finitely presented groups

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.

The Modular Group A Finitely Generated Group with Interesting Subgroups

The action of Möbius transformations with real coefficients preserves the hyperbolic metric in the upper half-plane model of the hyperbolic plane. The modular group is an interesting group of hyperbolic isometries generated by two Möbius transformations, namely, an order-two element, g2 HzL = -1 ê z, and an element of infinite order, g• HzL = z + 1. Viewing the action of the group elements on a...

A characterization of finitely generated multiplication modules

 Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

Periodic rings with finitely generated underlying group

We study periodic rings that are finitely generated as groups. We prove several structure results. We classify periodic rings that are free of rank at most 2, and also periodic rings R such that R is finitely generated as a group and R/t(R) Z. In this way, we construct new classes of periodic rings. We also ask a question concerning the connection to periodic rings that are finitely generated a...

Ring With All Finitely Generated Modules Retractable