On pseudo-codecomposition of a transformation group

TL;DR

This paper introduces the concept of pseudo-codecomposition in transformation groups, establishing an intermediate class between all transformation groups and those codecomposable to distal ones, expanding the theoretical framework of group transformations.

Contribution

It defines pseudo-codecomposition for transformation groups and characterizes the intermediate class between all groups and those codecomposable to distal groups.

Findings

Pseudo-codecomposition is introduced as a new concept.

The collection of pseudo-codecomposable groups forms a proper intermediate class.

The class of all groups pseudo-codecomposable to distal groups is characterized.

Abstract

In the following text we introduce the concept of pseudo-codecomposition of a transformation group, also we show the collection of all transformation groups pseudo-codecomposable to distal ones is a proper intermediate class of the class of all transformation groups and the class of all transformation groups codecomposable to distal ones.