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1.
Let KGbe the group algebra of a p1 -group Gover a field Kof characteristic p > 0, and let U(KG)be its group of units. If KGcontains a nontrivial bicyclic unit and if Kis not algebraic over its prime field, then we prove that the free product Zp? Zp? Zpcan be embedded in U(KG).  相似文献   

2.
We show that if G is a definably compact, definably connected definable group defined in an arbitrary o‐minimal structure, then G is divisible. Furthermore, if G is defined in an o‐minimal expansion of a field, k ∈ ? and pk : GG is the definable map given by pk (x ) = xk for all xG , then we have |(pk )–1(x )| ≥ kr for all xG , where r > 0 is the maximal dimension of abelian definable subgroups of G . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
Let G be a reductive linear algebraic group over an algebraically closed field K, let P? be a parabolic subgroup scheme of G containing a Borel subgroup B, and let P = P?red ? P? be its reduced part. Then P is reduced, a variety, one of the well known classical parabolic subgroups. For char(K) = p > 3, a classification of the P?'s has been given in [W1]. The Chow ring of G/P only depends on the root system of G. Corresponding to the natural projection from G/P to G/P? there is a map of Chow rings from A(G/P?) to A(G/P). This map will be explicitly described here. Let P = B, and let p > 3. A formula for the multiplication of elements in A(G/P?) will be derived. We will prove that A(G/P?) ? A(G/P) (abstractly as rings) if and only if G/P ? G/P? as varieties, i. e., the Chow ring is sensitive to the thickening. Furthermore, in certain cases A(G/P?) is not any more generated by the elements corresponding to codimension one Schubert cells.  相似文献   

4.
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 HK ⩽ 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 PG 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   

5.
M. Asaad 《代数通讯》2013,41(11):4217-4224
Let G be a finite group. A subgroup K of a group G is called an ?-subgroup of G if N G (K) ∩ K x  ≦ K for all x ? G. The set of all ?-subgroups of G will be denoted by ?(G). Let P be a nontrivial p-group. A chain of subgroups 1 = P 0 ? P 1 ? ··· ? P n  = P is called a maximal chain of P provided that |P i : P i?1| = p, i = 1, 2, ···, n. A nontrivial p-subgroup P of G is called weakly supersolvably embedded in G if P has a maximal chain 1 = P 0 ? P 1 ? ··· ? P i  ? ··· ? P n  = P such that P i  ? ?(G) for i = 1, 2, ···, n. Using the concept of weakly supersolvably embedded, we obtain new characterizations of p-nilpotent and supersolvable finite groups.  相似文献   

6.
David I. Stewart 《代数通讯》2013,41(12):4702-4716
Let G be the simple, simply connected algebraic group SL 3 defined over an algebraically closed field K of characteristic p > 0. In this article, we find H 2(G, V) for any irreducible G-module V. When p > 7, we also find H 2(G(q), V) for any irreducible G(q)-module V for the finite Chevalley groups G(q) = SL(3, q) where q is a power of p.  相似文献   

7.
LetG be a simply connected nilpotent Lie group. IfK andH are closed connected subgroups which intersect only in the neutral element, the multiplicationK ×H G is shown to be a proper mapping. Furthermore, we consider the operation ofK ×H onG given byg · (k, h)=k –1 gh. It is shown that, under certain assumptions, this operation is proper if and only if it is free. Under more restrictive assumptions, the quotientKG/H is diffeomorphic to an n .  相似文献   

8.
An automorphismϕ of a groupG is said to be uniform il for everygG there exists anhG such thatG=h −1 h ρ . It is a well-known fact that ifG is finite, an automorphism ofG is uniform if and only if it is fixed-point-free. In [7] Zappa proved that if a polycyclic groupG admits an uniform automorphism of prime orderp thenG is a finite (nilpotent)p′-group. In this paper we continue Zappa’s work considering uniform automorphism of orderpg (p andq distinct prime numbers). In particular we prove that there exists a constantμ (depending only onp andq) such that every torsion-free polycyclic groupG admitting an uniform automorphism of orderpq is nilpotent of class at mostμ. As a consequence we prove that if a polycyclic groupG admits an uniform automorphism of orderpq thenZ μ (G) has finite index inG.
Al professore Guido Zappa per il suo 900 compleanno  相似文献   

9.
10.
Let G be a connected reductive Lie group and K be a maximal compact subgroup of G. We prove that the semigroup of all K-biinvariant probability measures on G is a strongly stable Hungarian semigroup. Combining with the result [see Rusza and Szekely(9)], we get that the factorization theorem of Khinchin holds for the aforementioned semigroup. We also prove that certain subsemigroups of K-biinvariant measures on G are Hungarian semigroups when G is a connected Lie group such that Ad G is almost algebraic and K is a maximal compact subgroup of G. We also prove a p-adic analogue of these results.  相似文献   

11.
Letp be an odd prime,K a field, andG K its absolute Galois group. It is shown thatK isp-adically closed if and only ifG K is isomorphic to an open subgroup of . It is also shown that if , withq=p r, thenK has a non-trivial henselian valuation.  相似文献   

12.
Xianbiao Wei 《代数通讯》2013,41(10):3410-3417
A subgroup H of a finite group G is said to be s-permutable in G if H permutes with every Sylow subgroup of G. In this article, some sufficient conditions for a finite group G to be p-nilpotent are given whenever all subgroups with order p m of a Sylow p-subgroup of G are s-permutable for a given positive integer m.  相似文献   

13.
Pablo Spiga 《代数通讯》2013,41(7):2540-2545
Let K be a field of characteristic p > 0, K* the multiplicative group of K and G = G p  × B a finite group, where G p is a p-group and B is a p′-group. Denote by K λ G a twisted group algebra of G over K with a 2-cocycle λ ∈Z 2(G, K*). In this article, we give necessary and sufficient conditions for K λ G to be of OTP representation type, in the sense that every indecomposable K λ G-module is isomorphic to the outer tensor product V#W of an indecomposable K λ G p -module V and an irreducible K λ B-module W.  相似文献   

14.
In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G p |<∞ (of course, it contains G = G p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞.  相似文献   

15.
Let G be a p[[t]]-standard group of level 1. Then G is p[[t]]-perfect if its lower central series is given by powers of the maximal ideal (p, t), i.e. if n(G) = G((p,t)n). We prove that a p[[t]]-perfect group is linear by imitating the proof that a p[[t]]-standard group is linear.  相似文献   

16.
Juping Tang 《代数通讯》2013,41(5):1913-1922
A subgroup H of G is called ? p -supplemented in G if there exists a subgroup B of G such that G = HB and TB < G for every maximal subgroup T of H with |H: T| =p α. In this paper, we investigate the influence of ? p -supplemented subgroup and some conditions for p-nilpotency and p-supersolvability of finite groups are obtained.  相似文献   

17.
Donald L. White 《代数通讯》2013,41(8):2907-2921
Let G be a finite group and let cd (G) be the set of irreducible character degrees of G. The degree graph Δ(G) is the graph whose set of vertices is the set of primes that divide degrees in cd (G), with an edge between p and q if pq divides a for some degree a ? cd (G). We determine the graph Δ(G) for the finite simple groups of types A ?(q) and 2 A ? (q 2), that is, for the simple linear and unitary groups.  相似文献   

18.
M. Asaad 《代数通讯》2013,41(10):4564-4574
Let G be a finite group and H a subgroup of G. We say that H is an ?-subgroup in G if NG(H) ∩ Hg ≤ H for all g ∈ G; H is called weakly ?-subgroup in G if G has a normal subgroup K such that G = HK and HK is an ?-subgroup in G. We say that H is weakly ? -embedded in G if G has a normal subgroup K such that HG = HK and HK is an ?-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that some subgroups of prime power order are weakly ?-embedded in G. Our results improve and generalize several recent results in the literature.  相似文献   

19.
Yangming Li  Liyun Miao 《代数通讯》2017,45(8):3468-3474
Let G be a finite group, E a normal subgroup of G and p a fixed prime. We say that E is p-hypercyclically embedded in G if every p-G-chief factor of E is cyclic. A subgroup H of G is said to satisfy Π-property in G if |GK:NGK((HL)KK)| is a π((HL)KK)-number for any chief factor LK in G; we say that H has Π*-property in G if HOπ(H)(G) has Π-property in G. In this paper, we prove that E is p-hypercyclically embedded in G if and only if some classes of p-subgroups of E have Π*-property in G. Some recent results are extended.  相似文献   

20.
In this article we prove that a set of points B of PG(n, 2) is a minimal blocking set if and only if ?B? = PG(d, 2) with d odd and B is a set of d + 2 points of PG(d, 2) no d + 1 of them in the same hyperplane. As a corollary to the latter result we show that if G is a finite 2-group and n is a positive integer, then G admits a ? n+1-cover if and only if n is even and G? (C 2) n , where by a ? m -cover for a group H we mean a set 𝒞 of size m of maximal subgroups of H whose set-theoretic union is the whole H and no proper subset of 𝒞 has the latter property and the intersection of the maximal subgroups is core-free. Also for all n < 10 we find all pairs (m,p) (m > 0 an integer and p a prime number) for which there is a blocking set B of size n in PG(m,p) such that ?B? = PG(m,p).  相似文献   

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