We study the problem concerning the influence of indices of maximal subgroups of a simple group on the structure of a group. We obtain a characterization property of all finite simple groups. 相似文献
It is shown explicitly how self-similar graphs can be obtained as `blow-up' constructions of finite cell graphs . This yields a larger family of graphs than the graphs obtained by discretising continuous self-similar fractals.
For a class of symmetrically self-similar graphs we study the simple random walk on a cell graph , starting at a vertex of the boundary of . It is proved that the expected number of returns to before hitting another vertex in the boundary coincides with the resistance scaling factor.
Using techniques from complex rational iteration and singularity analysis for Green functions, we compute the asymptotic behaviour of the -step transition probabilities of the simple random walk on the whole graph. The results of Grabner and Woess for the Sierpinski graph are generalised to the class of symmetrically self-similar graphs, and at the same time the error term of the asymptotic expression is improved. Finally, we present a criterion for the occurrence of oscillating phenomena of the -step transition probabilities.
For G a finite group, πe(G) denotes the set of orders of elements in G. If Ω is a subset of the set of natural numbers, h(Ω) stands for the number of isomorphism classes of finite groups with the same set Ω of element orders. We say that G is k-distinguishable if h(πe(G)) = k < ∞, otherwise G is called non-distinguishable. Usually, a 1-distinguishable group is called a characterizable group. It is shown that if M is a sporadic simple group different from M12, M22, J2, He, Suz, McL and O′N, then Aut(M) is characterizable by its element orders. It is also proved that if M is isomorphic to M12, M22, He, Suz or O′N, then h(πe(Aut(M))) ∈¸ {1,∞}. 相似文献
Under certain constraints on the characteristic of a field , the commutative standard enveloping q-algebra >B of a commutative triple system A over is defined. It is proved that(1) if the algebra B is simple, then the system A is simple;(2) if the system A is simple, then B either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals). 相似文献
We introduce the notion of tracial topological rank for C*-algebras.In the commutative case, this notion coincides with the coveringdimension. Inductive limits of C*-algebrasof the form PMn(C(X))P,where X is a compact metric space with dim Xk, and P is aprojection in Mn(C(X)), have tracial topological rank no morethan k. Non-nuclear C*-algebras can have small tracial topologicalrank. It is shown that if A is a simple unital C*-algebra withtracial topological rank k (< ), then
(i) A is quasidiagonal,
(ii) A has stable rank 1,
(iii) A has weakly unperforatedK0(A),
(iv) A has the following Fundamental Comparabilityof Blackadar:if p, qA are two projections with (p) < (q)for all tracialstates on A, then pq
Define a ringA to be RRF (respectively LRF) if every right (respectively left)A-module is residually finite. We determine the necessary and sufficient conditions for a formal triangular matrix ring
to be RRF (respectively LRF). Using this we give examples of RRF rings which are not LRF. 相似文献
The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property
of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function
of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented
as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix
theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution
function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when
there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain
time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources. 相似文献
Let G = SL(n, q), where q is odd, V be a natural module over G, and L = S2(V) be its symmetric square. We construct a 2-cohomology group H2(G, L). The group is one-dimensional over Fq if n = 2 and q ≠ 3, and also if (n, q) = (4, 3). In all other cases H2(G, L) = 0. Previously, such groups H2(G, L) were known for the cases where n = 2 or q = p is prime. We state that H2(G, L) are trivial for n ⩾ 3 and q = pm, m ⩾ 2. In proofs, use is made of rather elementary (noncohomological) methods.
__________
Translated from Algebra i Logika, Vol. 47, No. 6, pp. 687–704, November–December, 2008. 相似文献