TY - JOUR

T1 - Palindromic automorphisms of free nilpotent groups

AU - Bardakov, Valeriy G.

AU - Gongopadhyay, Krishnendu

AU - Neshchadim, Mikhail V.

AU - Singh, Mahender

N1 - Publisher Copyright: © 2016 Elsevier B.V.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84994851790&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2016.06.011

DO - 10.1016/j.jpaa.2016.06.011

M3 - Article

AN - SCOPUS:84994851790

VL - 221

SP - 316

EP - 338

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 2

ER -