共查询到20条相似文献，搜索用时 0 毫秒
1.
In this article, it is shown that the normalizer property holds for the following two kinds of finite nilpotent-by-nilpotent groups: (1) G = NwrH is the standard wreath product of N by H, where N is a finite nilpotent group and H is a finite abelian 2-group; (2) G is a finite group having a normal nilpotent subgroup N such that the integral group ring ?(G/N) has only trivial units. Our results generalize a result of Yuanlin Li and extend some ones obtained by Juriaans, Miranda, and Robério. 相似文献
2.
Zhengxing Li 《代数通讯》2013,41(9):3933-3938
Let N be a finite nontrivial nilpotent group and H a finite centerless permutation group on a finite set Ω (i.e., H acts faithfully on Ω). Let G = N?H = N|Ω| ? H be the corresponding permutational wreath product of N by H. It is shown that every Coleman automorphism of G is an inner automorphism. This generalizes a well-known result due to Petit Lobão and Sehgal stating that the normalizer property holds for complete monomial groups with nilpotent base groups. 相似文献
3.
Let G = N?Q be a semidirect product of a finite 2-closed group N by a rational group Q. It is shown that under some conditions the normalizer property holds for G. 相似文献
4.
Let K be a finite abelian group and let H be the holomorph of K. It is shown that every Coleman automorphism of H is an inner automorphism. As an immediate consequence of this result, it is obtained that the normalizer property holds for H. 相似文献
5.
Víctor Jiménez López 《代数通讯》2013,41(1):63-76
Hirano studied the quasi-Armendariz property of rings, and then this concept was generalized by some authors, defining quasi-Armendariz property for skew polynomial rings and monoid rings. In this article, we consider unified approach to the quasi-Armendariz property of skew power series rings and skew polynomial rings by considering the quasi-Armendariz condition in mixed extension ring [R; I][x; σ], introducing the concept of so-called (σ, I)-quasi Armendariz ring, where R is an associative ring equipped with an endomorphism σ and I is an σ-stable ideal of R. We study the ring-theoretical properties of (σ, I)-quasi Armendariz rings, and we obtain various necessary or sufficient conditions for a ring to be (σ, I)-quasi Armendariz. Constructing various examples, we classify how the (σ, I)-quasi Armendariz property behaves under various ring extensions. Furthermore, we show that a number of interesting properties of an (σ, I)-quasi Armendariz ring R such as reflexive and quasi-Baer property transfer to its mixed extension ring and vice versa. In this way, we extend the well-known results about quasi-Armendariz property in ordinary polynomial rings and skew polynomial rings for this class of mixed extensions. We pay also a particular attention to quasi-Gaussian rings. 相似文献
6.
Martin Hertweck 《Proceedings Mathematical Sciences》2008,118(2):189-195
For the alternating group A 6 of degree 6, Zassenhaus’ conjecture about rational conjugacy of torsion units in integral group rings is confirmed. Dedicated to the memory of I. S. Luthar Professor Luthar died at the age of 74 in December 2006. 相似文献
7.
Martin Hertweck 《代数通讯》2013,41(9):3224-3229
It is shown that in the units of augmentation one of an integral group ring ? G of a finite group G, a noncyclic subgroup of order p 2, for some odd prime p, exists only if such a subgroup exists in G. The corresponding statement for p = 2 holds by the Brauer–Suzuki theorem, as recently observed by Kimmerle. 相似文献
8.
Mazur猜想:具有阿贝尔Sylow 2-子群的有限群有正规化子性质.设G是一个有限群,N是G的一个正规子群且Z(G/N)仅有平凡单位,本文建立了由Z(G/N)中单位诱导的G的自同构与N的Coleman自同构之间的联系,在此基础上证明了若G是一个具有阿贝尔Sylow 2-子群的有限群且Z(G/F*(G))仅有平凡单位,则Mazur猜想对G成立. 相似文献
9.
Coleman Automorphisms of Extensions of Finite Characteristically Simple Groups by Some Finite Groups
Let G be an extension of a finite characteristically simple group by an abelian group or a finite simple group.It is shown that every Coleman automorphism of G is an inner automorphism.Interest in such automorphisms arises from the study of the normalizer problem for integral group rings. 相似文献
10.
V. A. Bovdi 《代数通讯》2013,41(7):2670-2680
We investigate the classical Zassenhaus conjecture for the unit group of the integral group ring of Mathieu simple group M 23 using the Luthar–Passi method. This work is a continuation of the research that we carried out for Mathieu groups M 11 and M 12. As a consequence, for this group we confirm Kimmerle's conjecture on prime graphs. 相似文献
11.
Let G be a finite group and let N be a nilpotent normal subgroup of G such that G/N is cyclic. It is shown that under some conditions all Coleman automorphisms of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings. 相似文献
12.
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
13.
Let G=Hol(H) be the holomorph of a finite group H. If there is a prime q dividing |H| such that every q-central automorphism of H is inner and Z(H)=1, then every Coleman automorphism of G is inner. In particular, the normalizer property holds for G. 相似文献
14.
We have described the structure of Q n (G) = Δ n (G)/Δ n+1(G) for 35 particular classes of groups G with order 25 in the previous article. In this article, the structure of Q n (G) for all the remaining classes of groups G with order 25 are presented. 相似文献
15.
16.
LetZG be the integral group ring of a groupG and I(G) its augmentation ideal. For a free groupF andR a normal subgroup ofF, the intersectionI
n+1 (F) ∩I
n+1 (R) is determined for alln≥ 1. The subgroupsF ∩ (1+ZFI (R) I (F) I (S)) ANDF ∩ (1 + I (R)I
3 (F)) of F are identified whenR and S are arbitrary subgroups ofF. 相似文献
17.
Andreas Bächle 《代数通讯》2013,41(10):4341-4349
For a group G and a subgroup H of G, this article discusses the normalizer of H in the units of a group ring RG. We prove that H is only normalized by the “obvious” units, namely products of elements of G normalizing H and units of RG centralizing H, provided H is cyclic. Moreover, we show that the normalizers of all subgroups of certain nilpotent and metacyclic groups in the corresponding group rings are as small as possible. These classes contain all dihedral groups, all finite nilpotent groups, and all finite groups with all Sylow subgroups being cyclic. 相似文献
18.
一类环上HX环的结构 总被引：9，自引：2，他引：9
自李洪兴１９９１年提出了ＨＸ环以来，人们一直有这么一个问题没解决，就是是否存在非平凡的ＨＸ环的例子？但至今既没找到非平凡的ＨＸ环，也没有证明任一环Ｒ仅存在平凡的ＨＸ环。针对这个问题，本文提出并证明了一类环仅有平凡ＨＸ环，还给出了一系列的结构定理。这样，既为证明任一环Ｒ仅有平凡的ＨＸ环的猜想有新的启示，也为人们指明无须在这一类环上寻找非平凡ＨＸ环。 相似文献
19.
In this article we construct free groups and subgroups of finite index in the unit group of the integral group ring of a finite non-Abelian group G for which every nonlinear irreducible complex representation is of degree 2 and with commutator subgroup G′ a central elementary Abelian 2-group. 相似文献
20.
In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ?[G] satisfies the multiplicative Jordan decomposition (MJD). In the nonabelian case, we show that ?[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27. 相似文献