共查询到20条相似文献,搜索用时 156 毫秒
1.
O. Yu. Dashkova 《Siberian Advances in Mathematics》2013,23(2):77-83
Let A be an R G-module over a commutative ring R, where G is a group of infinite section p-rank (0-rank), C G (A) = 1, A is not a Noetherian R-module, and the quotient A/C A (H) is a Noetherian R-module for every proper subgroup H of infinite section p-rank (0-rank). We describe the structure of solvable groups G of this type. 相似文献
2.
Yu Qing Chen 《Discrete Mathematics》2008,308(13):2764-2775
In this paper, we give a characterization of a group G which contains a semiregular relative difference set R relative to a central subgroup N containing the commutator subgroup [G,G] of G such that 1∈R and rRr=R for all r∈R. In particular, these relative difference sets are fixed by inversion and inner automorphisms of the group are multipliers. We also present a construction of such relative difference sets. 相似文献
3.
We establish the existence of universal G-spaces for proper actions of locally compact groups on Tychonoff spaces. A typical result sounds as follows: for each infinite cardinal number τ every locally compact, non-compact, σ-compact group G of weight w(G)?τ, can act properly on Rτ?{0} such that Rτ?{0} contains a G-homeomorphic copy of every Tychonoff proper G-space of weight ?τ. The metric cones Cone(G/H) with H⊂G a compact subgroup such that G/H is a manifold, are the main building blocks in our approach. As a byproduct we prove that the cardinality of the set of all conjugacy classes of such subgroups H⊂G does not exceed the weight of G. 相似文献
4.
A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = HK. In the paper it is proved that a finite group G is p-nilpotent provided p is the smallest prime number dividing the order of G and every minimal subgroup of P∩G′ is weakly-supplemented in N G (P), where P is a Sylow p-subgroup of G. As applications, some interesting results with weakly-supplemented minimal subgroups of P∩G′ are obtained. 相似文献
5.
S. F. Kamornikov 《Mathematical Notes》2010,87(3-4):372-379
The paper deals with finite solvable groups only. It is established that the class of all regular subgroup m-functors coincides with the class of all X-abnormal m-functors, where X ranges over all subclasses of the class of all primitive groups. The properties of the lattice of all regular subgroup m-functors are studied and the atoms and coatoms of this lattice are described. It is proved that the generalized Frattini subgroup of G corresponding to a regularm-functor coincides with the X-coradical of G for some R 0-closed class X. 相似文献
6.
Chris Woodcock 《Journal of Pure and Applied Algebra》2007,210(1):193-199
Throughout, all rings R will be commutative with identity element. In this paper we introduce, for each finite group G, a commutative graded Z-algebra RG. This classifies the G-invariant commutative R-algebra multiplications on the group algebra R[G] which are cocycles (in fact coboundaries) with respect to the standard “direct sum” multiplication and have the same identity element.In the case when G is an elementary Abelian p-group it turns out that RG is closely related to the symmetric algebra over Fp of the dual of G. We intend in subsequent papers to explore the close relationship between G and RG in the case of a general (possibly non-Abelian) group G.Here we show that the Krull dimension of RG is the maximal rank r of an elementary Abelian subgroup E of G unless either E is cyclic or for some such E its normalizer in G contains a non-trivial cyclic group which acts faithfully on E via “scalar multiplication” in which case it is r+1. 相似文献
7.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(12):1333-1338
Let G be the group of real points of a reductive algebraic ℚ-group satisfying the same assumptions as in [5], Chapter I, and let Γ be a discrete subgroup of G. Let RΓ be the right regular representation of G in L2(Γ\G). We prove in this Note that, for any integrable rapidly decreasing function ƒ on G, the restriction of RΓ(ƒ) to the discrete spectrum of RΓ is a trace class operator. 相似文献
8.
Finite <Emphasis Type="Italic">p</Emphasis>-groups with a class of complemented normal subgroups 下载免费PDF全文
Assume G is a finite group and H a subgroup of G. If there exists a subgroup K of G such that G = HK and H ∩ K = 1, then K is said to be a complement to H in G. A finite p-group G is called an NC-group if all its proper normal subgroups not contained in Φ(G) have complements. In this paper, some properties of NC-groups are investigated and some classes of NC-groups are classified. 相似文献
9.
Ramesh Gangolli 《Journal of Functional Analysis》1977,25(3):244-252
Let G be a locally compact motion group, i.e., it is a semidirect product of a compact subgroup with a closed abelian normal subgroup, the action of the compact subgroup on the other one being by conjugation. The main result of this paper is that the group algebra of such a group is symmetric. This result is then used to prove that a generalization of the Wiener-Tauberian theorem holds for such groups. Precisely, it is shown that every proper closed two-sided ideal in L1(G) is annihilated by an irreducible unitary representation of G, lifted to L1(G). 相似文献
10.
Let G be a finite group,and H a subgroup of G.H is called s-permutably embedded in G if each Sylow subgroup of H is a Sylow subgroup of some s-permutable subgroup of G.In this paper,we use s-permutably embedding property of subgroups to characterize the p-supersolvability of finite groups,and obtain some interesting results which improve some recent results. 相似文献
11.
Let G be a finite group, and let A be a proper subgroup of G. Then any chief factor H/A G of G is called a G-boundary factor of A. For any Gboundary factor H/A G of A, the subgroup (A ∩ H)/A G of G/ A G is called a G-trace of A. In this paper, we prove that G is p-soluble if and only if every maximal chain of G of length 2 contains a proper subgroup M of G such that either some G-trace of M is subnormal or every G-boundary factor of M is a p′-group. This result give a positive answer to a recent open problem of Guo and Skiba. We also give some new characterizations of p-hypercyclically embedded subgroups. 相似文献
12.
t Let F = Cay(G, S), R(G) be the right regular representation of G. The graph Г is called normal with respect to G, if R(G) is normal in the full automorphism group Aut(F) of F. Г is called a bi-normal with respect to G if R(G) is not normal in Aut(Г), but R(G) contains a subgroup of index 2 which is normal in Aut(F). In this paper, we prove that connected tetravalent edge-transitive Cayley graphs on PGL(2,p) are either normal or bi-normal when p ≠ 11 is a prime. 相似文献
13.
Yutaka Hiramine 《Discrete Mathematics》2008,308(13):2776-2780
Let G be a group of order 4n and t an involution of G. A 2n-subset R of G is called a left Hadamard transversal of G with respect to 〈t〉 if G=R〈t〉 and for some subsets S1 and S2 of G. Let H be a subgroup of G such that G=[G,G]H, t∈H, and tG⊄H, where tG is the conjugacy class of t and [G,G] is the commutator subgroup of G. In this article, we show that if R satisfies a condition , then R is a (2n,2,2n,n) relative difference set and one can construct a v×v integral matrix B such that BBT=BTB=(n/2)I, where v is a positive integer determined by H and tG (see Theorem 2.6). Using this we show that there is no left Hadamard transversal R satisfying (*) in some simple groups. 相似文献
14.
Let G be a connected semisimple real algebraic group. Assume that G(R) has no compact factors and let Γ be a torsion-free uniform lattice subgroup of G(R). Then Γ contains a malnormal abelian subgroup A. This implies that the II1 factor VN(Γ) contains a masa A with Pukánszky invariant {∞}. 相似文献
15.
Let X be an affine algebraic variety with a transitive action of the algebraic automorphism group. Suppose that X is equipped with several fixed point free nondegenerate SL2-actions satisfying some mild additional assumption. Then we prove that the Lie algebra generated by completely integrable
algebraic vector fields on X coincides with the space of all algebraic vector fields. In particular, we show that apart from a few exceptions this fact
is true for any homogeneous space of form G/R where G is a linear algebraic group and R is a closed proper reductive subgroup of G. 相似文献
16.
A subgroup H of a finite group G is said to be complemented in G if there exists a subgroup K of G such that G=HK and H∩K=1. In this paper, it is proved that a finite group G is p-nilpotent provided p is the smallest prime number dividing the order of G and every minimal subgroup of the p-focal subgroup of G is complemented in NG(P), where P is a Sylow p-subgroup of G. As some applications, some interesting results related with complemented minimal subgroups of focal subgroups are obtained. 相似文献
17.
Salvador Hernández Sergio Macario F. Javier Trigos-Arrieta 《Journal of Mathematical Analysis and Applications》2008,348(2):834-842
If H is a dense subgroup of G, we say that H determines G if their groups of characters are topologically isomorphic when equipped with the compact open topology. If every dense subgroup of G determines G, then we say that G is determined. The importance of this property is justified by the recent generalizations of Pontryagin-van Kampen duality to wider classes of topological Abelian groups. Among other results, we show (a) ⊕i∈IR determines the product ∏i∈IR if and only if I is countable, (b) a compact group is determined if and only if its weight is countable. These answer questions of Comfort, Raczkowski and the third listed author. Generalizations of the above results are also given. 相似文献
18.
Hong Pan 《Czechoslovak Mathematical Journal》2018,68(4):1051-1054
A subgroup H of a finite group G is weakly-supplemented in G if there exists a proper subgroup K of G such that G = HK. In the paper, we extend one main result of Kong and Liu (2014). 相似文献
19.
Marja Kankaanrinta 《Topology and its Applications》2005,153(4):610-619
Assume G is a Lie group, K is a compact subgroup of G and M is a proper smooth G-manifold. Using properties of the regular representations L2(G) and L2(K), we first prove results about extending certain representations and embedding homogeneous spaces smoothly into Hilbert G-spaces. We then prove that M can be embedded as a closed smooth G-invariant submanifold of some Hilbert G-space. It follows that M admits a complete G-invariant smooth Riemannian metric. 相似文献
20.
Nikolai Gordeev 《Journal of Pure and Applied Algebra》2009,213(2):250-258
We obtain the following characterization of the solvable radical R(G) of any finite group G: R(G) coincides with the collection of all g∈G such that for any 3 elements a1,a2,a3∈G the subgroup generated by the elements , i=1,2,3, is solvable. In particular, this means that a finite group G is solvable if and only if in each conjugacy class of G every 4 elements generate a solvable subgroup. The latter result also follows from a theorem of P. Flavell on {2,3}′-elements in the solvable radical of a finite group (which does not use the classification of finite simple groups). 相似文献