Groebner-Shirshov basis for HNN extensions of groups and for the alternating group

TL;DR

This paper extends the theory of Groebner-Shirshov bases to compute normal forms for HNN extensions of groups and the alternating group, broadening algebraic computational methods.

Contribution

It generalizes Shirshov's Composition Lemma by replacing the monomial order, enabling new normal form calculations for complex group extensions.

Findings

Normal forms for HNN extensions derived

Normal forms for the alternating group obtained

Generalization of Shirshov's Composition Lemma achieved

Abstract

In this paper, we generalize the Shirshov's Composition Lemma by replacing the monomial order for others. By using Groebner-Shirshov bases, the normal forms of HNN extension of a group and the alternating group are obtained.