共查询到20条相似文献,搜索用时 19 毫秒
1.
A. L. Myl’nikov 《Siberian Mathematical Journal》2007,48(5):879-883
A subset K of some group G is called twisted if 1 ∈ K and xy ?1 x ∈ K for all x, y ∈ K. We study the finite twisted subsets with an involution which are not subgroups but whose every proper twisted subset is a subgroup. We also consider the groups generated by twisted subsets. 相似文献
2.
A subset K of some group C is called twisted if 1 ∈ K and x, y ∈ K implies that xy ?1 x belongs to K. We use the concept of twisted subset to investigate and generalize the concept of involutory decomposition of a group. A group is said to admit involutory decomposition if it contains some involution such that the group is the product of the centralizer of the involution and the set of elements inverted by the involution. We study the twisted subsets with at most one involution. We prove that if a twisted subset has no involutions at all then it generates a subgroup of odd order. 相似文献
3.
We prove that a group generated by a twisted subset is finite and its order is bounded by some function depending only on the order of the twisted subset. 相似文献
4.
A. L. Myl’nikov 《Siberian Mathematical Journal》2006,47(5):915-923
We study finite groups whose every subset containing the identity and closed with respect to the operation x ○ y = xy ?1 x is a subgroup. We prove that the derived subgroup of such a group is nilpotent, which implies that the derived length of such a group is at most three. 相似文献
5.
Finite tangled groups 总被引:2,自引:2,他引:0
A. L. Myl’nikov 《Siberian Mathematical Journal》2007,48(2):295-299
We study the so-called finite tangled groups. These are the groups whose every subset containing 1 and closed under the operation x ○ y = xy ?1 x is a subgroup. The general problem of studying such groups reduces to the case of tangled groups of odd order. We classify all finite nilpotent tangled groups. 相似文献
6.
A. L. Myl’nikov 《Mathematical Notes》2010,88(5-6):860-867
A subset K of a group G is said to be twisted if 1 ∈ K and the element xy ?1 x lies in K for any x, y ∈ K. We study finite involution-free twisted subsets that are not subgroups but all of whose proper twisted subsets are subgroups. We also study the groups generated by such twisted subsets. 相似文献
7.
An involution v of a group G is said to be finite (in G) if vv
g
has finite order for any g ∈ G. A subgroup B of G is called a strongly embedded (in G) subgroup if B and G\B contain involutions, but B ∩ B
g
does not, for any g ∈ G\B. We prove the following results. Let a group G contain a finite involution and an involution whose centralizer in G is periodic. If every finite subgroup of G of even order is contained in a simple subgroup isomorphic, for some m, to L
2(2
m
) or Sz(2
m
), then G is isomorphic to L
2(Q) or Sz(Q) for some locally finite field Q of characteristic two. In particular, G is locally finite (Thm. 1). Let a group G contain a finite involution and a strongly embedded subgroup. If the centralizer of some involution in G is a 2-group, and every finite subgroup of even order in G is contained in a finite non-Abelian simple subgroup of G, then G is isomorphic to L
2(Q) or Sz(Q) for some locally finite field Q of characteristic two (Thm. 2).
Supported by RFBR (project No. 08-01-00322), by the Council for Grants (under RF President) and State Aid of Leading Scientific
Schools (grant NSh-334.2008.1), and by the Russian Ministry of Education through the Analytical Departmental Target Program
(ADTP) “Development of Scientific Potential of the Higher School of Learning” (project Nos. 2.1.1.419 and 2.1.1./3023). (D.
V. Lytkina and V. D. Mazurov)
Translated from Algebra i Logika, Vol. 48, No. 2, pp. 190–202, March–April, 2009. 相似文献
8.
The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of
Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras
with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution
is adjoint to a Pfister form. Moreover, cohomological invariants of those algebras with involution are discussed. 相似文献
9.
In this paper we present two cyclic Gray codes for signed involutions. The first one has a natural construction, implemented by a CAT algorithm, based in the recursive formula for the number of signed involutions. The second code, although with a higher computational cost, has the smallest possible Hamming distance for this family of objects. 相似文献
10.
GAO Hongzhu & GUO Ren School of Mathematical Science Beijing Normal University Beijing China 《中国科学A辑(英文版)》2005,48(12):1631-1636
Let σ be an anti-holomorphic involution on an almost complex four manifold X, a necessary and sufficient condition is given to determine weather X/σ admits an almost complex structure. 相似文献
11.
Hongzhu Gao 《中国科学A辑(英文版)》1989,42(6):586-592
Let σ be an anti-holomorphic involution on almost complex manifoldX, the existence of almost complex structure onY=X/σ is discussed.
Project supported by the National Natural Science Foundation of China (Grant No. 19771010). 相似文献
12.
Axel Hultman 《Transactions of the American Mathematical Society》2007,359(6):2787-2798
The open intervals in the Bruhat order on twisted involutions in a Coxeter group are shown to be PL spheres. This implies results conjectured by F. Incitti and sharpens the known fact that these posets are Gorenstein over .
We also introduce a Boolean cell complex which is an analogue for twisted involutions of the Coxeter complex. Several classical Coxeter complex properties are shared by our complex. When the group is finite, it is a shellable sphere, shelling orders being given by the linear extensions of the weak order on twisted involutions. Furthermore, the -polynomial of the complex coincides with the polynomial counting twisted involutions by descents. In particular, this gives a type-independent proof that the latter is symmetric.
13.
We present a general construction of involutions on integer partitions which enables us to prove a number of modulo 2 partition congruences. 相似文献
14.
AbstractA sufficient and necessary condition for the reducibility of the Verma modules over the twisted Yangians of rank one is given. 相似文献
15.
Jae Choon Cha 《Transactions of the American Mathematical Society》2003,355(10):4187-4200
We study the twisted Alexander invariants of fibred knots. We establish necessary conditions on the twisted Alexander invariants for a knot to be fibred, and develop a practical method to compute the twisted Alexander invariants from the homotopy type of a monodromy. It is illustrated that the twisted Alexander invariants carry more information on fibredness than the classical Alexander invariants, even for knots with trivial Alexander polynomials.
16.
17.
Dante DeBlassie Robert Smits 《Transactions of the American Mathematical Society》2005,357(3):1245-1274
The tail behavior of a Brownian motion's exit time from an unbounded domain depends upon the growth of the ``inner radius' of the domain. In this article we quantify this idea by introducing the notion of a twisted domain in the plane. Roughly speaking, such a domain is generated by a planar curve as follows. As a traveler proceeds out along the curve, the boundary curves of the domain are obtained by moving out units along the unit normal to the curve when the traveler is units away from the origin. The function is called the growth radius. Such domains can be highly nonconvex and asymmetric. We give a detailed account of the case , . When , a twisted domain can reasonably be interpreted as a ``twisted cone.'
18.
John Kalliongis Darryl McCullough 《Transactions of the American Mathematical Society》1996,348(5):1739-1755
The observation that the quotient orbifold of an orientation- reversing involution on a 3-dimensional handlebody has the structure of a compression body leads to a strong classification theorem, and general structure theorems. The structure theorems decompose the action along invariant discs into actions on handlebodies which preserve the -fibers of some -bundle structure. As applications, various results of R. Nelson are proved without restrictive hypotheses.
19.
Xiao-yuan Chen 《高校应用数学学报(英文版)》2008,23(3):366-370
Results of the research for smash product algebras over dimodule algebras are generalized to the more general twisted dimodule algebras. 相似文献
20.