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A note on class-preserving automorphisms#br#

GUO Ji-dong1, HAI Jin-ke2*   

  1. 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000,  Xinjiang, China;
    2. College of Mathematics, Qingdao University, Qingdao 266071, Shandong, China
  • Received:2013-11-28 Online:2014-06-20 Published:2014-06-14

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Abstract: Let G be a semidirect product of a cyclic group C and a 2-group P of maximal class. If a Sylow 2-subgroup of G has an abelian subgroup of index 2. It is shown that every class-preserving automorphism of G is an inner automorphism. In particular, the normalizer property holds for G.

Key words: class-preserving automorphisms, the normalizer problem, integral group rings

[1] HAI Jin-ke, WANG Wei, HE Wei-ping. A note on Coleman automorphisms of finite groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 35-38.
[2] HAI Jin-ke, LI Zheng-xing. On central automorphisms and class-preserving
automorphisms of finite groups [J]. J4, 2011, 46(6): 1-3.
[3] HAI Jin-ke, LI Zheng-xing, DU Gui-qing. A note on class-preserving automorphisms of finite groups [J]. J4, 2010, 45(12): 28-30.
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