Journal of Shanghai University(Natural Science Edition) ›› 2017, Vol. 23 ›› Issue (5): 714-721.doi: 10.12066/j.issn.1007-2861.1744

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Finite p-groups with central automorphism almost being inner automorphism

ZHANG Boru, GUO Xiuyun   

  1. College of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2016-01-06 Online:2017-10-30 Published:2017-10-30

Abstract:

Let G be a finite p-group and let K(G) be a subgroup of G consisting of all elements in G fixed by every central automorphism in G. A necessary and sufficient
condition is given on |Autc(G) : Inn(G)| = |Z(G) : K(G)| for a finite p-group G of class 2. The condition for |Autc(G) : Inn(G)| = p|Z(G) : K(G)| is also studied.

Key words: central kernel, inner automorphism, central automorphism