On commutativity and finiteness in groups

The second author introduced notions of weak permutablity and commutativity between groups and proved the finiteness of a group generated by two weakly permutable finite subgroups. Two groups H, K weakly commute provided there exists a bijection f: H → K which fixes the identity and such that h commutes with its image h ^f for all h ∈ H. The present paper gives support to conjectures about the nilpotency of groups generated by two weakly commuting finite abelian groups H, K.      

特征非2半质环的交换性定理

给出了特征非2半质环的几个交换性定理.     

Coincidence Points and Invariant Approximation Results for Multimaps

Some coincidence point theorems satisfying a general contractive condition are proved. As applications, some invariant approximation results are also obtained and several related results in the literature are either extended or improved.     

素环的对称双导

本文讨论了具有非零对称双导的素环的交换性,得到了完善的定理,从而改进了已有的结果.     

Wightman axiomatic approach in noncommutative field theory

The axiomatic approach based on Wightman functions is developed in noncommutative field theory. We prove that the main results of the axiomatic approach remain valid if the noncommutativity affects only the spatial variables.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 403#x2013;416, February, 2005.     

CERTAIN COMMUTATIVITY CONDITIONS FOR RINGS WITH UNITY

ＣＥＲＴＡＩＮＣＯＭＭＵＴＡＴＩＶＩＴＹＣＯＮＤＩＴＩＯＮＳＦＯＲＲＩＮＧＳＷＩＴＨＵＮＩＴＹＶ．Ｗ．Ｊａｃｏｂ，Ｍ．ＡｓｈｒａｆａｎｄＭ．Ａ．Ｑｕａｄｒｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓＡｌｉｇａｒｈＭｕｓｌｉｍＵｎｉｖｅｒｓｉｔ...     

Wigner定理在保持算子乘积范数正映射的应用

把Wigner定理应用于算子代数上的保持映射问题,证明了如果φ是标准算子代数上的正映射,且保持两个算子乘积的范数或奇异值的和,则φ必定具有形式φ(A)=UAU*,其中U是一个酉算子或反酉算子.     

Coincidence and fixed points for hybrid strict contractions

We define the property (E.A) for single-valued and multivalued mappings and introduce the notion of T-weak commutativity for a hybrid pair (f,T) of single-valued and multivalued maps. We obtain some coincidence and fixed point theorems for this class of maps and derive, as application, an approximation theorem.     

On strong reality of the unipotent Lie-type subgroups over a field of characteristic 2

A group G is called strongly real if its every nonidentity element is strongly real, i.e. conjugate with its inverse by an involution of G. We address the classical Lie-type groups of rank l, with l ≤ 4 and l ≤ 13, over an arbitrary field, and the exceptional Lie-type groups over a field K with an element η such that the polynomial X ² + X + η is irreducible either in K[X] or K ₀[X] (in particular, if K is a finite field). The following question is answered for the groups under study: What unipotent subgroups of the Lie-type groups over a field of characteristic 2 are strongly real?     

Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements

Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n×n matrices and the group of all 2n×2n symplectic matrices over F, respectively. A linear operator L:M2n(F)→M2n(F) is said to preserve the symplectic group if L(SP2n(F))=SP2n(F). It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form (i) L(X)=QPXP-1 for any X∈M2n(F) or (ii) L(X)=QPXTP-1 for any X∈M2n(F), where Q∈SP2n(F) and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3(1975), 715-724.