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power automorphism
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  幂自同构
     (3) G= PH, in which P ∈Sylp(G), p = min(π(G )), H is abelian, and P can not acttrivially on any non-trivial subgroup of H, and every non-identity element of P induces a power automorphism of Hby conjugating.
     (2)G=PH,其中P∈Sylp,(G),p=min(π(G)),H是Abel群,并且P不能平凡作用于H的任一≠1的子群,P的每个≠1的元诱导H的一个幂自同构
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  “power automorphism”译为未确定词的双语例句
     In this paper, we show that if a finite group G has a fixed-point-free weak power automorphism, then G is a Dedekind group.
     本文给出了Dedekind群的一个刻画.即如果一个群G有一个无不动点的弱幂同构,则G是一个Dedekind群
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  相似匹配句对
     POWER
     清华的力量
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     power;
     权力 ;
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     Automorphism of Hypergroups
     幂群的内自同构
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  power automorphism
Several examples ofp-groups having large power automorphism groups are given.
      
It is proved that the nilpotence class of a metabelianp-group of exponentp2 possessing a nontrival power automorphism is bounded by a function ofp.
      


The main purpose of the present paper is proving the following two theorems: I. For a finite groupG, the following statements are equivalent: (1)every Sylow group of G is semi-normal; (2)every subgroup of G issemi-normal ; (3)every subgroup of G is S-semi-normal; (4) every Sylow subgroup of G is strong-semi-normal;(5)every subgroup of G is semi-normal or self-normal ; (6)every subgroup of G is S -semi-normal or self-normal;(7) G is generalized nilpotent ; let H/K be any chief factor of G, G/CG(H/K) is a cyclic...

The main purpose of the present paper is proving the following two theorems: I. For a finite groupG, the following statements are equivalent: (1)every Sylow group of G is semi-normal; (2)every subgroup of G issemi-normal ; (3)every subgroup of G is S-semi-normal; (4) every Sylow subgroup of G is strong-semi-normal;(5)every subgroup of G is semi-normal or self-normal ; (6)every subgroup of G is S -semi-normal or self-normal;(7) G is generalized nilpotent ; let H/K be any chief factor of G, G/CG(H/K) is a cyclic group of order a primePower which is coprime with |H/K|. Ⅱ. For a finite group G, the following three statements are equivalent: (1)every subgroup of Cis S -semi-normal or self-normal, and C has truly self-normal Sylow subgroups; (2) G=PH,p ∩H = 1, in which, P ∈sylp(G), p = min(π(G)), NG(P) = P, H = K∞(G ), is the nilpotent residual of G,and KG, K ≤ H; (3) G= PH, in which P ∈Sylp(G), p = min(π(G )), H is abelian, and P can not acttrivially on any non-trivial subgroup of H, and every non-identity element of P induces a power automorphism of Hby conjugating.

本文的主要目的是证明如下两个定理:Ⅰ.对于有限群G,下列命题等价:(1)G的sylow子群皆半正规;(2)G的子群皆半正规;(3)G的子群皆S-半正规;(4)G的Sylow子群皆强半正规;(5)G的子群皆半正规或自正规;(6)G的子群皆S-半正规或自正规;(7)G是广幂零群;令H/K是G的任一主因子,则G/CG(H/K)是阶与|H/K|互素的素数幂阶循环群.Ⅱ.对于有限群G,下列命题等价:(1)G的子群皆S-半正规或自正规,且G确有自正规的Sylow子群;(2)G=PH,P∩H=1.其中P∈Sylp,(G),P=min(π(G)),NG(P)=P,H=K∞(G)是G的幂零剩余,并且K≤H,均有K G;(2)G=PH,其中P∈Sylp,(G),p=min(π(G)),H是Abel群,并且P不能平凡作用于H的任一≠1的子群,P的每个≠1的元诱导H的一个幂自同构.

In this paper,it is shown that a finite group G is abelian if and only if G satisfies the following conditions : (Ⅰ) G has a power automorphism Q such that C_G(a) is an elementary abelian 2-group. (Ⅱ )G has no subgroup isomorphic to 2-group < a,b|a~2~n= b~2~m = 1,a~b = a~1+2~(n+1) > where n ≥ 3 and n≥m. In addition, applying the above result, the author also proves that if a finite group G has a power automorphism Q such that C_G(a) is an elementary abelian 2-group, then G is nilpotent.

本文证明了有限群G是Abel群当且仅当G_r满足下列条件:(Ⅰ) G有一个幂自同构 a使得 CG(a)是一个初等 AbelZ一群.(Ⅱ)G没有子群与2-群<a,b|a~2~n=b~2~m=1,a~b=a~(1+2)~(n-1)>同构,其中n≥3,n≥m.利用该结果,作者还证明若有限群G有一个幂自同构a使得C_G(a)是一个初等Abel2-群,则G是幂零群

In this paper, we show that if a finite group G has a fixed-point-free weak power automorphism, then G is a Dedekind group.

本文给出了Dedekind群的一个刻画.即如果一个群G有一个无不动点的弱幂同构,则G是一个Dedekind群

 
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