On Engel Elements of a Group Relative to Certain Subgroup

Abstract

An element g in a group G is called a left Engel element of G, if for each x ∈ G, there is a positive integer n = n(g, x) such that [x, _n g] = 1. In this article, we will study a generalization of the left Engel elements and its connections with the generalized Hirsch–Plotkin and Baer radical.

Key Words:

• Baer radical
• Hirsch-Plotkin radical
• Left engel
• Right engel

2000 Mathematics Subject Classification:

• Primary 20F45

Notes

Communicated by A. Turull.