In some finiteness conditions , we prove that there exists a natural abelian group homomorphism from the grothendieck group of r to the grothendieck group of a . in particular , the homomorphism is splitting if p is quasi - n - tilting 在适当的有限性条件下,我们证明了一个从r的grothendieck群到a的orothendieck群的自然的阿贝尔群同态。
Because of the non - abelian feature of strong interaction theory , it can not describe non - perturbative effect , so phenomenological models provide the main study method for relativistic nucleon - nucleon collisions 由于强相互作用理论的非abelian性,它不能定量描述非微扰效)许,所以唯象理论模型是目前研究相对论性核一核碰撞的主要斤法之。
The first part deals with the construction of semisymmetric graphs and the second part classifies the edge - transitive regular coverings of the cube , whose covering transformation groups are iso - morphic to the elementary abelian p - groups 第一部分是关于半对称图的分类,第二部分是关于立方体边传递的正则覆盖图的分类,其覆盖变换群同构于初等交换p -群。
In terms of sub - shifts of finite type determined by an irreducible matrix , affine maps of compacted connected metric abelian group and continuous maps of tree , the two concepts of topologically ergodic map and topologically transitive map are identical 指出对于由不可约方阵所决定的符号空间有限型子转移而言,或紧致交换群的仿射变换及树上连续自映射而言,拓扑遍历与拓扑可迁这两个概念是一致的。
Theorem 2 . 4 let g be a non - abelian inner - finite group , each non - trivial proper subgroup of g is prime order cyclic group if and only if g is a simple group ; each proper subgroup of g is nilpotent ; and each non - trivial subgroup of g is self - normalizer 4设g是非阿贝尔的内有限群,则g的每个非平凡真子群都是素数阶循环群的充分必要条件是g是单群, g的每个真子群幂零且g的每个非平凡的真子群自正规化定理2
In this paper , at first we study the inner - finite core - finite group in section 2 . by investigating the inner - finite infinite simple groups , we have proved : theorem 2 . 2 let g be a non - abelian inner - finite group and g = < a , b > . if one of a and b is an involution , then g is not a simple group 2设g是由a和b两元生成的非阿贝尔的内有限群,若a和b两元中有对合,则z ( g )含对合,因而g非单群;而且g不是内阿贝尔的。
With this method , in the present thesis , we will classify all the connected regular covering graphs of the cube satisfying the following two properties : ( 1 ) the covering transformation group is isomorphic to the elementary abelian p - group ; ( 2 ) the group of fibre - preserving automorphisms acts edge - transitively 本文中,我们用同一种方法分类立方体的正则连通覆盖图,并且满足两个条件,覆盖变换群同构于初等交换p -群且保纤维自同构群是边传递的。
Theorem 2 . 5 let g be an infinite simple group that satisfies maximal condition . g is an inner - finite group and each non - trivial proper subgroup of g is abelian if and only if for each x in g , cg ( x ) is the only maximal subgroup that contain x . s * ( a * , c * ) - groups can be regarded as a generalizations of dedekind groups , since all of dedekind groups are s * ( a * , c * ) - groups 5设g是满足极大条件的无限单群,则g是内有限群,而且g的每个非平凡真子群是阿贝尔群的充分必要条件是对g的任意非平凡元x ,有c _ g ( x )是g的含x的唯一极大子群且c _ g ( x )是有限的。