A new approach to connect algebra with analysis: Relationships and applications between presentations and generating functions

Abstract

For a minimal group (or monoid) presentation P, let us suppose that P satisfies the algebraic property of either being efficient or inefficient. Then one can investigate whether some generating functions can be applied to it and study what kind of new properties can be obtained by considering special generating functions. To establish that, we will use the presentations of infinite group and monoid examples, namely the split extensions Zn Zand Z2 Z, respectively. This study will give an opportunity to make a new classification of infinite groups and monoids by using generating functions. © 2013 Gao and Gao; licensee Springer.