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151.
Noam Agmon 《Theoretical chemistry accounts》1986,70(3):203-219
The irreducible characters of a finite group are determined uniquely by those of a minimal set of maximal subgroups. The method is based on the construction of all class functions which are irreducible characters on every maximal subgroup. These are generalized characters by a theorem of Brauer, so that the irreducible characters are obtained by checking the norm. An alternative characterization of irreducible characters, the Maximum Mixing Rule, works for all point symmetry groups, and its physical significance is discussed. As an example, the character tables for all point symmetry groups and crystal double-groups are constructed in this way.Bat-Sheva de Rothschild fellow for 1985 相似文献
152.
We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S
4-free and every minimal subgroup of P ∩ G
N is c-supplemented in N
G(P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized. 相似文献
153.
Anthony Bak 《K-Theory》1991,4(4):363-397
A functorial filtration GL
n
=S–1L
n
S0L
n
S
i
L
n
E
n of the general linear group GL
n, n 3, is defined and it is shown for any algebra A, which is a direct limit of module finite algebras, that S–1 L
n
(A)/S0L
n
(A) is abelian, that S0L
n
(A)
S1L
n
(A)
is a descending central series, and that S
i
L
n
(A) = E
n(A) whenever i the Bass-Serre dimension of A. In particular, the K-functors k
1 S
i
L
n
=S
i
L
n
/E
n are nilpotent for all i 0 over algebras of finite Bass-Serre dimension. Furthermore, without dimension assumptions, the canonical homomorphism S
i
L
n
(A)/S
i+1 L
n
(A)S
i
L
n+ 1(A)/S
i+1
L
n + 1 (A) is injective whenever n i + 3, so that one has stability results without stability conditions, and if A is commutative then S0L
n
(A) agrees with the special linear group SL
n
(A), so that the functor S0L
n
generalizes the functor SL
n
to noncommutative rings. Applying the above to subgroups H of GL
n
(A), which are normalized by E
n(A), one obtains that each is contained in a sandwich GL
n
(A, )
H
E
n(A, ) for a unique two-sided ideal of A and there is a descending S0L
n
(A)-central series GL
n
(A, )
S0L
n
(A, )
S1L
n
(A, )
S
i
L
n
(A, )
E
n(A, ) such that S
i
L
n
(A, )=E
n(A, ) whenever i Bass-Serre dimension of A.Dedicated to Alexander Grothendieck on his sixtieth birthday 相似文献
154.
155.
《数学季刊》2016,(4):406-411
Let F be a saturated formation of finite groups. Given a proper subgroup H of a group G, a subgroup H of G is called F-normal in G if G/HG belongs to F;otherwise H is said to be F-abnormal in G. In this paper, we investigate the structure of a finite group byθ?-completions of F-abnormal subgroups. 相似文献
156.
Let G be a group and let K be a field of characteristic p>0. Lie nilpotent group algebras of strong Lie nilpotency index up to 11 have already been classified. In this paper, our aim is to classify the group algebras KG which are strongly Lie nilpotent of index 12 or 13. 相似文献
157.
We extend our analysis of the symmetry content of the classical polyhedra [1] to the analysis of the degree of polyhedral subgroup symmetries. The quantitative levels of the hierarchical polyhedral symmetries series of Oh, D4h and D2h of hexacoordinated structures, as well as the relations between them, serve as an example. A distinction is made between two types of measures: quantitative evaluation of the degree of symmetry, and quantitative evaluation of the degree of content of a reference shape. 相似文献
158.
群G的子群H称为半置换的,若对任意的K≤G,只要(|H|,|K|)=1.就有HK=KH,H称为s-半置换的,若对任意的p‖G|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文利用Sylow子群的2-极大子群的s-半置换性得到有限群为p-幂零群的一些充分条件. 相似文献
159.
关于T-S模的超直觉模糊群及其同态 总被引:2,自引:0,他引:2
本文研究了关于T-S模的直觉模糊正规子群、超直觉模糊群、超直觉模糊正规子群和直觉模糊商群,利用T模、S模的定义及性质,在两个经典群同态的意义下,获得了关于超直觉模糊群的同态与同构等若干结果. 相似文献
160.
New characterizations of finite supersoluble groups 总被引:13,自引:0,他引:13
Let A be a subgroup of a group G and X a nonempty subset of G.A is called an X- semipermutable subgroup of G if A has a supplement T in G such that for every subgroup T_1 of T there exists an clement x∈X such that AT_i~x=T_i~xA.On the basis of this concept we obtain some new characterizations of finite supersoluble groups. 相似文献