共查询到20条相似文献,搜索用时 15 毫秒
1.
Peter Danchev 《Periodica Mathematica Hungarica》2009,59(1):37-42
Let G be a p-reduced Abelian group and R a commutative unital ring of prime characteristic p such that for each natural number i the subring $
R^{p^i }
$
R^{p^i }
has nilpotent elements. It is shown that if S(RG) is the normalized Sylow p-group in the group ring RG, then S(RG) is torsion-complete if and only if G is a bounded p-group. This strengthens our former results on this subject. 相似文献
2.
Consider a finite group G. A subgroup is called S-quasinormal whenever it permutes with all Sylow subgroups of G. Denote by B
sG
the largest S-quasinormal subgroup of G lying in B. A subgroup B is called S-supplemented in G whenever there is a subgroup T with G = BT and B∩T ≤ B
sG
. A subgroup L of G is called a quaternionic subgroup whenever G has a section A/B isomorphic to the order 8 quaternion group such that L ≤ A and L ∩ B = 1. This article is devoted to proving the following theorem. 相似文献
3.
A subgroup H of a finite group
G is called c-normal in
G if there exists a normal subgroup
N of G such that
G = HN and $H \cap N \leq H_{G} = {\rm core}_{G}(H)$. In this paper, we investigate the class of groups
of which every maximal subgroup of its Sylow
p-subgroup is c-normal and the
class of groups of which some minimal subgroups of its Sylow
p-subgroup is c-normal for some prime number
p. Some interesting results are obtained and
consequently, many known results related to
p-nilpotent groups and
p-supersolvable groups are generalized. 相似文献
4.
E. I. Bunina 《Journal of Mathematical Sciences》2010,169(5):557-588
In this paper, we prove that every automorphism of a Chevalley group of type B l , l ≥ 2, over a commutative local ring with 1/2 is standard, i.e., it is a composition of ring, inner, and central automorphisms. 相似文献
5.
All groups considered in this paper will be finite. Our main result here is the following theorem. Let G be a solvable group in which the Sylow p-subgroups are either bicyclic or of order p
3 for any p ∈ π(G). Then the derived length of G is at most 6. In particular, if G is an A4-free group, then the following statements are true: (1) G is a dispersive group; (2) if no prime q ∈ π(G) divides p
2 + p + 1 for any prime p ∈ π(G), then G is Ore dispersive; (3) the derived length of G is at most 4. 相似文献
6.
In this paper we classify the p-local finite groups over p1+2+, the extraspecial group of order p3 and exponent p for odd p. This study reduces to the classification of the saturated fusion systems over p1+2+, which will be characterized by the outer automorphism group, the number of -radical subgroups and the automorphism group of each nontrivial -radical subgroup. As part of this classification, we obtain three new exotic 7-local finite groups.Partially supported by MCYT grant BFM2001-2035.Partially supported by MCYT grant BFM2001-1825.Both authors have been supported by the EU grant nr HPRN-CT-1999-00119.in final form: 1 October 2003 相似文献
7.
A finite group G is called p
i
-central of height k if every element of order p
i
of G is contained in the k
th
-term ζ
k
(G) of the ascending central series of G. If p is odd, such a group has to be p-nilpotent (Thm. A). Finite p-central p-groups of height p − 2 can be seen as the dual analogue of finite potent p-groups, i.e., for such a finite p-group P the group P/Ω1(P) is also p-central of height p − 2 (Thm. B). In such a group P, the index of P
p
is less than or equal to the order of the subgroup Ω1(P) (Thm. C). If the Sylow p-subgroup P of a finite group G is p-central of height p − 1, p odd, and N
G
(P) is p-nilpotent, then G is also p-nilpotent (Thm. D). Moreover, if G is a p-soluble finite group, p odd, and P ∈ Syl
p
(G) is p-central of height p − 2, then N
G
(P) controls p-fusion in G (Thm. E). It is well-known that the last two properties hold for Swan groups (see [11]). 相似文献
8.
We show a simple way to determine purity for a B(n)-group contained in a completely decomposable group. 相似文献
9.
X. Yi 《Siberian Mathematical Journal》2010,51(3):435-438
We find the cases in which a finite p-soluble group with a special Sylow p-subgroup has p-length 1. 相似文献
10.
Let k be a field finitely generated over ℚ and p a prime. The torsion conjecture (resp. p-primary torsion conjecture) for abelian varieties over k predicts that the k-rational torsion (resp. the p-primary k-rational torsion) of a d-dimensional abelian variety A over k should be bounded only in terms of k and d. These conjectures are only known for d=1. The p-primary case was proved by Y. Manin, in 1969; the general case was completed by L. Merel, in 1996, after a series of contributions
by B. Mazur, S. Kamienny and others. Due to the fact that moduli of elliptic curves are 1-dimensional, the d=1 case of the torsion conjecture (resp. p-primary torsion conjecture) is closely related to the following. For any k-curve S and elliptic scheme E→S, the k-rational torsion (resp. the p-primary k-rational torsion) is uniformly bounded in the fibres E
s
, s∈S(k). In this paper, we extend this result in the p-primary case to arbitrary abelian schemes over curves. 相似文献
11.
Let p be an odd prime number and let n be an arbitrary positive integer. We prove that there exists a p-group whose mod-p cohomology ring has a nilpotent element H2() satisfying n0,n+p–1=0. As a corollary, we exhibit a p-group whose mod-p cohomology ring contains an element of nilpotency degree n+1.Mathematical Subject Classification (2000): 20J06, 20D15, 55R40To Phuong and Nin 相似文献
12.
V. S. Atabekyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2011,46(5):237-242
There is a well-known fact, that any group G
1 is a CEP-subgroup both for the direct product G
1 × G
2 and the free productG
1 * G
2 of G
1 with any group G
2. The paper gives a necessary and sufficient condition providing that a multiplier G
i
of a n-periodic product Π
i∈I
n
G
i
of any family of groups {G
i
}
i∈I
is a CEP-subgroup. Particularly, the found criterionmeans that any group G
1 of odd period n ≥ 665 is a CEP-subgroup of the n-periodic product Π
i∈I
n
G
i
for any group G
2. 相似文献
13.
A subgroup H of a finite group G is said to be c*-supplemented in G if there exists a subgroup K such that G = HK and H ⋂ K is permutable in G. It is proved that a finite group G that is S
4-free is p-nilpotent if N
G
(P) is p-nilpotent and, for all x ∈ G\N
G
(P), every minimal subgroup of
is c*-supplemented in P and (if p = 2) one of the following conditions is satisfied: (a) every cyclic subgroup of
of order 4 is c*-supplemented in P, (b)
, (c) P is quaternion-free, where P a Sylow p-subgroup of G and
is the p-nilpotent residual of G. This extends and improves some known results.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1011–1019, August, 2007. 相似文献
14.
Dong-il Lee 《Algebras and Representation Theory》2010,13(6):705-718
In this note, we find a monomial basis of the cyclotomic Hecke algebra \({\mathcal{H}_{r,p,n}}\) of G(r,p,n) and show that the Ariki-Koike algebra \({\mathcal{H}_{r,n}}\) is a free module over \({\mathcal{H}_{r,p,n}}\), using the Gröbner-Shirshov basis theory. For each irreducible representation of \({\mathcal{H}_{r,p,n}}\), we give a polynomial basis consisting of linear combinations of the monomials corresponding to cozy tableaux of a given shape. 相似文献
15.
N. Memić 《P-Adic Numbers, Ultrametric Analysis, and Applications》2016,8(2):149-159
We establish results concerning ergodicity on compact subsets of Z p and study ergodicity of polynomials on subsets of Z2 and Z3. 相似文献
16.
Zhangjia Han 《Proceedings Mathematical Sciences》2010,120(2):141-148
A subgroup H of a group is said to be s-semipermutable in G if it is permutable with every Sylow p-subgroup of G with (p, |H|) = 1. Using the concept of s-semipermutable subgroups, some new characterizations of p-nilpotent groups are obtained and several results are generalized. 相似文献
17.
Christine Bessenrodt 《Archiv der Mathematik》2007,89(1):1-9
Starting from the question when all irreducible p-Brauer characters for a symmetric or an alternating group are of p-power degree, we classify the p-modular irreducible representations of p-power dimension in some families of representations for these groups. In particular, this then allows to confirm a conjecture
by W. Willems for the alternating groups.
Received: 14 June 2006 相似文献
18.
A subgroup K of G is Mp-supplemented in G if there exists a subgroup B of G such that G = KB and TB < G for every maximal subgroup T of K with |K: T| = pα. In this paper we prove the following: Let p be a prime divisor of |G| and let H be ap-nilpotent subgroup having a Sylow p-subgroup of G. Suppose that H has a subgroup D with Dp ≠ 1 and |H: D| = pα. Then G is p-nilpotent if and only if every subgroup T of H with |T| = |D| is Mp-supplemented in G and NG(Tp)/CG(Tp) is a p-group. 相似文献
19.
We give an example of a short exact sequence 1NGD1 of pro-p groups such that the cohomological dimension cd(G)=2, G is (topologically) finitely generated, N is a free pro-p group of infinite rank, D is a Demushkin group, for every closed subgroup S of G containing N and any natural number n the inflation map is an isomorphism but G is not a free pro-p product of a free pro-p group by a Demushkin group. This is a group theoretic version of a question raised by T. Würfel for some special Galois groups.Both authors are partially supported by bolsa de produtividade de pesquisa from CNPq, Brazil and CNPq grant 470272/2003-1. 相似文献
20.
J. A. Ryan 《Siberian Mathematical Journal》2007,48(2):311-316
A Coxeter system (W, S) is said to be of type K n if the associated Coxeter graph ΓS is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by ΓS. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type K n then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W). 相似文献