n-th Relative nilpotency degree and relative n-isoclinism classes

TL;DR

This paper explores the concepts of relative n-isoclinism and n-th relative nilpotency degree, extending classical group theory notions to provide new insights into group classifications and properties.

Contribution

It introduces and analyzes the concepts of relative n-isoclinism and n-th relative nilpotency degree, expanding the theoretical framework of group theory.

Findings

Extended the notion of isoclinism to relative n-isoclinism.

Analyzed properties of n-th relative nilpotency degree.

Connected these concepts to group classification methods.

Abstract

P. Hall introduced the notion of isoclinism between two groups more than 60 years ago. Successively, many authors have extended such a notion in different contexts. The present paper deals with the notion of relative n-isoclinism, given by N. S. Hekster in 1986, and with the notion of n-th relative nilpotency degree, recently introduced in literature.