Some comparison results on equivalence groups

TL;DR

This paper compares two types of equivalence groups in differential equations, establishing subgroup relations and discussing implications for invariant functions, thereby clarifying their structural relationships.

Contribution

It provides a theoretical comparison of two equivalence group types, showing one as a subgroup of the other and analyzing consequences for invariant functions.

Findings

One type of equivalence group is a subgroup of the other.

The comparison yields new insights into invariant functions.

The results are formalized as theorems.

Abstract

This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be identified with a subgroup of the other type. Consequences of this comparison related in particular to the determination of invariant functions of the differential equations are also discussed.