Palindromic automorphisms of free nilpotent groups

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• 作者：Valeriy G. Bardakov^a ; ^b ; ^c ; ^{bardakov@math.nsc.ru" class="auth_mail" title="E-mail the corresponding author} ; Krishnendu Gongopadhyay^d ; ^{krishnendu@iisermohali.ac.in" class="auth_mail" title="E-mail the corresponding author} ; Mikhail V. Neshchadim^a ; ^{neshch@math.nsc.ru" class="auth_mail" title="E-mail the corresponding author} ; Mahender Singh^d ; ^{mahender@iisermohali.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary ; 20F28 ; secondary ; 20E36 ; 20E05
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：221
• 期：2
• 页码：316-338
• 全文大小：421 K

文摘

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.