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61.
Let G be a finite group, H ≤ G and R be a commutative ring with an identity 1R. Let CRG(H)={α ∈ RG|αh = hα for all h ∈ H), which is called the centralizer subalgebra of H in RG. Obviously, if H=G then CRG(H) is just the central subalgebra Z(RG) of RG. In this note, we show that the set of all H- conjugacy class sums of G forms an R-basis of CRG(H). Furthermore, let N be a normal subgroup of G and γthe natural epimorphism from G to G to G/N. Then γ induces an epimorphism from RG to RG, also denoted by % We also show that if R is a field of characteristic zero, then γ induces an epimorphism from CRG(H) to CRG(H), that is, 7(CRG(H)) = CRG(H). 相似文献
62.
姚炳学 《吉首大学学报(自然科学版)》2003,24(2):23-25,34
在(∈,∈∨q)-模糊子群的基础上,引入了(∈,∈∨q)-模糊正规化子与(∈,∈∨q)-模糊中心化子的概念,并讨论了它们的一些性质.同时,给出了(∈,∈∨q)-模糊商群与(∈,∈∨q)-模糊商子群的定义,建立了(∈,∈∨q)-模糊商群的同构定理. 相似文献
63.
The Commutativity Relation in the Symmetric Semigroup 总被引:1,自引:1,他引:0
We compute the cardinality of the centralizer of an injection or surjection provided that the basic set is countable. We prove a formula for the cardinality of the set of conjugacy classes in the infinite symmetric group. 相似文献
64.
Finite Groups with Character Degrees of Two Distinct Primes 总被引:1,自引:1,他引:0
CHEN Shengan FAN Yun SHUM Karpin 《武汉大学学报:自然科学英文版》2006,11(2):343-345
0Introduction Characterdegreesoffinitegroupsandtheirsubgroupshavebeenrecentlystudied[16].Inthisnote,westudytherelationshipsbetweenthegroup theoreticalstructureofafinitegroupGandthearithmeticpropertyofthedegreesofthe irreduciblecharactersofG.Afundamentalfactisthatifafi nitegroupGhasanabeliannormalsubgroupA,thenthede greeofanyirreduciblecharacterofGdividesthequotientorder|G/A|;seeTheorem6.15ofRef.[2]andProperty24of Ref.[7].ForfinitesolvablegroupsG,It gaveapartialin verse.Heshownthatifthede… 相似文献
65.
基于Hilbert空间H上的一个完全分配可交换子空间格代数Alg L,考虑Alg L上的中心化映射.设为Alg L上的一个可加映射,用完全分配可交换子空间格代数的结构性质和代数分解,证明了:若存在正整数m,n≥1,使得A∈Alg L,(Am+n+1)-Am(A)An∈F I成立,则存在Alg L中心里的元素λ,满足A∈Alg L,有(A)=λA. 相似文献
66.
67.
For partially commutative metabelian groups, annihilators of elements of commutator subgroups are described; canonical representations
of elements are defined; approximability by torsion-free nilpotent groups is proved; centralizers of elements are described.
Also, it is proved that two partially commutative metabelian groups have equal elementary theories iff their defining graphs
are isomorphic, and that every partially commutative metabelian group is embeddable in a metabelian group with decidable universal
theory.
Dedicated to V. N. Remeslennikov on the occasion of his 70th birthday
Supported by RFBR (project No. 09-01-00099).
Translated from Algebra i Logika, Vol. 48, No. 3, pp. 309–341, May–June, 2009. 相似文献
68.
69.
We obtain the decomposition of the tensor space
as a module for
, find an explicit formula for the multiplicities of its irreducible summands, and (when n 2k) describe the centralizer algebra
=
(
) and its representations. The multiplicities of the irreducible summands are derangement numbers in several important instances, and the dimension of
is given by the number of derangements of a set of 2k elements. 相似文献
70.
Janusz Konieczny 《Czechoslovak Mathematical Journal》2001,51(4):873-888
Second centralizers of partial transformations on a finite set are determined. In particular, it is shown that the second centralizer of any partial transformation consists of partial transformations that are locally powers of . 相似文献