On equality of central and class preserving automorphisms of finite\n p-groups

2011/06/02 by Deepak Gumber, Gumber, Deepak, Hemant Kalra +1
Social Sciences · #20D15 #20D45 #FOS: Mathematics #Group Theory (math.GR) #Japanese History and Culture #Migration, Ethnicity, and Economy

paper · pdf · doi:10.48550/arxiv.1106.0373

openalex publication_date 2011/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite non-abelian p-group, where p is a prime. Let\n\Aut_c(G) and \Aut_z(G) respectively denote the group of\nall class preserving and central automorphisms of G. We give a necessary\ncondition for G such that \Aut_c(G)=\Aut_z(G) and give\nnecessary and sufficient conditions for G with elementary abelian or cyclic\ncenter such that \Aut_c(G)=\Aut_z(G). We also characterize\nall finite p-groups G of order \≤ p⁷ such that\n\Aut_c(G)=\Aut_z(G) and complete the classification of all\nfinite p-groups of order \≤ p⁵ for which there exist non-inner class\npreserving automorphisms.\n

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