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21.
A proper subgroup H of a group G is said to be strongly embedded if 2 (H) and 2(HH
g) (for all
). An involution i of G is said to be finite if
(for all g G). As is known, the structure of a (locally) finite group possessing a strongly embedded subgroup is determined by the theorems of Burnside and Brauer--Suzuki, provided that the Sylow 2-subgroup contains a unique involution. In this paper, sufficient conditions for the equality m
2(G)= 1 are established, and two analogs of the Burnside and Brauer—Suzuki theorems for infinite groups G possessing a strongly embedded subgroup and a finite involution are given. 相似文献
22.
The construction of the sum of a direct (semilattice ordered) system of algebras introduced by J. Plonka – later known as the Plonka sum – is one of the most important methods of composition in universal algebra, having a number of applications in different algebraic theories, such as semigroup theory, semiring theory, etc. In this paper we present a more general way for constructing algebras with involution, that is, algebraic systems equipped with a unary involutorial operation which is at the same time an antiautomorphism of the underlying algebra. It is the sum – involutorial Plonka sum, as we call it – of an involution semilattice ordered system of algebras. We investigate its basic properties, as well as the problem of its subdirect decomposition. 相似文献
23.
Jan M. Aarts Robbert J. Fokkink 《Proceedings of the American Mathematical Society》2001,129(9):2803-2807
There is a close relation between the color number of a continuous map without fixed points and the topological dimension. If is an involution, the color number is also related to the co-index. An addition theorem for the color number is established thus underscoring the interrelations between color number, dimension and co-index.
24.
Let G be a complex semisimple group with real form G
. For the action of G
× G
on G by left and right translation, we define and study an orbit-type stratification of G. In particular, we compute the dimension of an arbitrary stratum; we identify certain strata of low codimension in G, the union of whose closures contains every nonprincipal stratum; and we describe the boundaries and adjacency relations of the maximal connected domains in G that contain only principal orbits. 相似文献
25.
LiPing Huang 《中国科学A辑(英文版)》2009,52(11):2404-2418
Let D be a division ring with an involution-,H2(D) be the set of 2 × 2 Hermitian matrices over D. Let ad(A,B) = rank(A-B) be the arithmetic distance between A,B ∈ H2(D) . In this paper,the fundamental theorem of the geometry of 2 × 2 Hermitian matrices over D(char(D) = 2) is proved:if :H2(D) → H2(D) is the adjacency preserving bijective map,then is of the form (X) = tP XσP +(0) ,where P ∈ GL2(D) ,σ is a quasi-automorphism of D. The quasi-automorphism of D is studied,and further results are obtained. 相似文献
26.
Homogeneous glasses in the Na2O–B2O3–Al2O3–SiO2 system doped with proper amount of AgCl were obtained by melting at a temperature of 1450 °C. Then, with several steps of treatment, including crystallization, elongation and reduction, the glass with oriented arrangement of needle-like micro–nano silver particles was produced. The microstructure and the optical properties of the glass samples in different stages were studied by SEM-EDAX, FE-SEM and UV–Vis spectrum. The results showed that the glass after elongation and reduction exhibits excellent polarization performance in the wavelength range from 600 nm to 900 nm, with an extinction ratio larger than 45 dB. The glass only elongated shows also slight polarizing performance, which may result from the formation of filament structure of Ag during elongation processing. 相似文献
27.
In the present note, we investigate schemes S in which each element s satisfies ns2 and ns*s≠2. We show that such a scheme is schurian. More precisely, we show that it is isomorphic to G//t, where G is a finite group and t an involution of G weakly closed in CG(t).
Groups G with an involution t weakly closed in CG(t) have been described in Glauberman's Z*-Theorem [G. Glauberman, Central elements in core-free groups, J. Algebra 4 (1966) 403–420] with the help of the largest normal subgroup of G having odd order. 相似文献
28.
Tomomi Kawamura 《Topology》2007,46(1):29-38
Rasmussen introduced a knot invariant based on Khovanov homology theory, and showed that this invariant estimates the four-genus of knots. We compare his result with the sharper slice-Bennequin inequality for knots. Then we obtain a similar estimate of the Rasmussen invariant for this inequality. 相似文献
29.
Ileana Streinu 《Computational Geometry》2005,31(3):195-206
We exhibit a family of graphs which can be realized as pseudo-visibility graphs of pseudo-polygons, but not of straight-line polygons. The example is based on the characterization of vertex-edge pseudo-visibility graphs of O'Rourke and Streinu [Proc. ACM Symp. Comput. Geometry, Nice, France, 1997, pp. 119–128] and extends a recent result of the author [Proc. ACM Symp. Comput. Geometry, Miami Beach, 1999, pp. 274–280] on non-stretchable vertex-edge visibility graphs. We construct a pseudo-visibility graph for which there exists a unique compatible vertex-edge visibility graph, which is then shown to be non-stretchable. The construction is then extended to an infinite family. 相似文献
30.
Nam-Hoon Lee 《Mathematische Nachrichten》2023,296(8):3449-3458
The concept of non-Gorenstein involutions on Calabi–Yau threefolds is a higher dimensional generalization of non-symplectic involutions on K3 surfaces. We present some elementary facts about Calabi–Yau threefolds with non-Gorenstein involutions. We give a classification of the Calabi–Yau threefolds of Picard rank one with non-Gorenstein involutions, whose fixed locus is not zero-dimensional. 相似文献