JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (2): 1-3.doi: 10.6040/j.issn.1671-9352.0.2013.250

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On the maximal π-factorable subnormal pairs

HAI Jin-ke, WANG Sheng-fang, LI Zheng-xing   

  1. School of Mathematics, Qingdao University, Qingdao 266071, Shandong, China
  • Received:2013-05-24 Online:2014-02-20 Published:2014-06-04


Based on existing results in the literature, the π-factorable subnormal pairs of π-separable groups are further discussed. It is proved that the automorphism group has an action on the set of maximal π-factorable subnormal pairs. As a direct result of the action, maximal π-factorable subnormal pairs are conjugate. In particular, Frattini argument of maximal π-factorable subnormal pairs is obtained.

Key words: π-separable groups, the maximal π-factorable subnormal pairs, π-factorable character

CLC Number: 

  • O152.1
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