A Generalization From Central Automorphism

The study of the automorphism group is an important research subject of group theory .At home and abroad a large number of relevant papers and monographs had appears, including the automorphism group of its own properties, and given a special kind of automorphism group of this group to determine the structure of demand. The former, such as [11] Zhou Zhongli, Qi Lili, Wen Jianwei. Circle Cn the automorphism group of [J], Chengdu University of Technology ,2007,689-691, [of 12] Shao Mingwen. P ~ 5 bands from the same group automorphism group order (Φ1-Φ5) [D], Guangxi University, master's thesis, 2002; The latter can be seen in [13] Zhang liang cai .On the automorphism group equations | Aut (G) | = 6r ~ 2 [D], Southwest China Normal University, master's thesis, 2003.The center of a group is a class of feature subgroup, the center automorphism is a subgroup of the automorphism, this is the starting point, in the center from the center of the same structure definition will extended to the characteristics of subgroups, and to make the concept of H ?automorphism . The center can be seen from the literature of the same structure:[1] ATYAR M S.On central automorphisms that fix the center element-wise[J].Arch.Math,2007,89:296-297.[2] YADAV M K.On central automorphisms fixing the center element-wise[EB/OL].(2008-03-28)[3] ROBINSON D J S.A course in the theory of groups[M].New York-Heidelberg-Berlin:Springer-Verlag,1982.[4] CURRAN M J,MCCAUGHAN D J.Central automorphisms that are almost inner[J].Comm.Algebra,2001,29(5):2081-2087.This article leads from the center automorphism and give feature automorphism concept .Further explore the nature of the role by a group act .let G is a group, HcharG .If g ? 1gα∈H, ?g∈G,we nameαas H ? automorphism of G .This definition is the development from central automorphism.Writing all H ? automorphism as H Aut ( G).Gave a theorem that Aut (G ) / H Aut ( G)< Aut (G / H) through a action from Aut(G) on G /H .