共查询到10条相似文献,搜索用时 140 毫秒
1.
Guo-ping TANG School of Mathematical Sciences Graduate University of Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2007,50(9):1280-1288
Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p~r,i.e.,a finite homocyclic abelian group.LetΔ~n (G) denote the n-th power of the augmentation idealΔ(G) of the integral group ring ZG.The paper gives an explicit structure of the consecutive quotient group Q_n(G)=Δ~n(G)/Δ~(n 1)(G) for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups. 相似文献
2.
Denote by D
m
the dihedral group of order 2m. Let ℛ(D
m
) be its complex representation ring, and let Δ(D
m
) be its augmentation ideal. In this paper, we determine the isomorphism class of the n-th augmentation quotient Δ
n
(D
m
)/Δ
n+1(D
m
) for each positive integer n. 相似文献
3.
4.
On a Problem of Karpilovsky 总被引:5,自引:0,他引:5
Let G be a finite elementary group. Let n (G) denote the nth power of the augmentation ideal (G) of the integral group ring G. In this paper, we give an explicit basis of the quotient group Qn(G) = n(G)/n+1 (G) and compute the order of Qn (G).2000 Mathematics Subject Classification: 16S34, 20C05 相似文献
5.
The definition of the group near-ring R[G] of the near-ring R over the group G as a near-ring of mappings from R
(G) to itself is due to Le Riche et al. (Arch Math 52:132–139, 1989). In this paper we consider the augmentation ideal Δ of R[G]. If the exponent of G is not 2, then the structure of ΔR
(G) is determined in terms of commutators and distributors. This is then used to show that Δ is nilpotent if and only if R is weakly distributive, has characteristic p
n
for some prime p and G is a finite p-group for the same prime p.
相似文献
6.
Raphael Yuster 《Graphs and Combinatorics》2001,17(3):579-587
We prove that for every ε>0 and positive integer r, there exists Δ0=Δ0(ε) such that if Δ>Δ0 and n>n(Δ,ε,r) then there exists a packing of K
n
with ⌊(n−1)/Δ⌋ graphs, each having maximum degree at most Δ and girth at least r, where at most εn
2 edges are unpacked. This result is used to prove the following: Let f be an assignment of real numbers to the edges of a graph G. Let α(G,f) denote the maximum length of a monotone simple path of G with respect to f. Let α(G) be the minimum of α(G,f), ranging over all possible assignments. Now let αΔ be the maximum of α(G) ranging over all graphs with maximum degree at most Δ. We prove that Δ+1≥αΔ≥Δ(1−o(1)). This extends some results of Graham and Kleitman [6] and of Calderbank et al. [4] who considered α(K
n
).
Received: March 15, 1999?Final version received: October 22, 1999 相似文献
7.
Let F n be the free group of rank n, and let Aut+(F n ) be its special automorphism group. For an epimorphism π : F n → G of the free group F n onto a finite group G we call the standard congruence subgroup of Aut+(F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ+(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ+(G, π) ≤ Aut+(F 2) has infinite abelianization. 相似文献
8.
Thomas P. Wakefield 《Algebras and Representation Theory》2011,14(4):609-623
Let G be a finite group and cd(G) be the set of irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G ≅ H×A, where A is an abelian group. In this paper, we verify the conjecture for the twisted Ree groups 2
G
2(q
2) for q
2 = 32m + 1, m ≥ 1. The argument involves verifying five steps outlined by Huppert in his arguments establishing his conjecture for many
of the nonabelian simple groups. 相似文献
9.
10.
In this article we present the nth power Δ n (G) of the augmentation ideal Δ(G) and describe the structure of Q n (G) = Δ n (G)/Δ n+1(G) for 35 particular groups G of order 25. The structure of Q n (G) for all the remaining groups of order 25 will be determined in a forthcoming article. 相似文献