Palindromic Automorphisms of Free Nilpotent Groups

TL;DR

This paper explores the structure of palindromic automorphisms in free nilpotent groups, establishing their group properties and providing generating sets for specific cases, advancing understanding of automorphism groups in algebra.

Contribution

It introduces the concept of palindromic automorphisms in free nilpotent groups and determines their generating sets for steps 2 and 3, including central automorphisms.

Findings

The set of palindromic automorphisms forms a group.

Generated automorphisms for step 2 and 3 free nilpotent groups.

Characterized central palindromic automorphisms satisfying tameness conditions.

Abstract

In this paper, we initiate the study of palindromic automorphisms of groups that are free in some variety. More specifically, we define palindromic automorphisms of free nilpotent groups and show that the set of such automorphisms is a group. We find a generating set for the group of palindromic automorphisms of free nilpotent groups of step 2 and 3. In particular, we obtain a generating set for the group of central palindromic automorphisms of these groups. In the end, we determine central palindromic automorphisms of free nilpotent groups of step 3 which satisfy the necessary condition of Bryant-Gupta-Levin-Mochizuki for a central automorphism to be tame.