Finitely generated $\mathfrak{N}$-semigroup and quotient group

Quotient Isomorphism Invariants of a Finitely Generated Coxeter Group

The isomorphism problem for finitely generated Coxeter groups is the problem of deciding if two finite Coxeter matrices define isomorphic Coxeter groups. Coxeter [4] solved this problem for finite irreducible Coxeter groups. Recently there has been considerable interest and activity on the isomorphism problem for arbitrary finitely generated Coxeter groups. In this paper we describe a family of...

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...

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...

Ring With All Finitely Generated Modules Retractable

MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...