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101.
In this paper I describe a local instructional theory for supporting the guided reinvention of the group and isomorphism concepts. This instructional theory takes the form of a sequence of key steps as students reinvent these fundamental group theoretic concepts beginning with an investigation of geometric symmetry. I describe these steps and frame them in terms of the theory of Realistic Mathematics Education. Each step of the local instructional theory is illustrated using samples of students’ written work or discussion excerpts. 相似文献
102.
103.
Let η be a non-zero scalar. In this paper, we investigate a bijective map ? between two von Neumann algebras, one of which has no central abelian projections, satisfying ?(AB+ηBA∗)=?(A)?(B)+η?(B)?(A)∗ for all A,B in the domain. It is showed that ? is a linear *-isomorphism if η is not real and ? is a sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real. 相似文献
104.
105.
106.
群的模糊同态与模糊商群的同构定理 总被引:8,自引:2,他引:6
利用模糊映射,给出群的模糊同态的概念,并得到模糊同态基本定理,同时建立模糊商群的同构定理。 相似文献
107.
In this note, we will give several examples to illustrate that two essential games which are isomorphic are not necessarily
S-equivalent when the cores of both games are “small” or empty. In other words, we show that whether two isomorphic games
are S-equivalent can not be justified in terms of the “size” of the core. 相似文献
108.
A solution of the isomorphism problem is presented for the class of Coxeter groups W that have a finite set of Coxeter generators S such that the underlying graph of the presentation diagram of the system (W,S) has the property that every cycle of length at least four has a chord. As an application, we construct counterexamples to
two conjectures concerning the isomorphism problem for Coxeter groups.
相似文献
109.
A group G is called a CI-group if, for any subsets S,T⊂ G, whenever two Cayley graphs Cay(G,S) and Cay(G,T) are isomorphic, there exists an element σ∊Aut(G) such that Sσ = T. The problem of seeking finite CI-groups is a long-standing open problem in the area of Cayley graphs. This paper contributes
towards a complete classification of finite CI-groups. First it is shown that the Frobenius groups of order 4p and 6p, and the metacyclic groups of order 9p of which the centre has order 3 are not CI-groups, where p is an odd prime. Then a shorter explicit list is given of candidates for finite CI-groups. Finally, some new families of
finite CI-groups are found, that is, the metacyclic groups of order 4p (with centre of order 2) and of order 8p (with centre of order 4) are CI-groups, and a proof is given for the Frobenius group of order 3p to be a CI-group, where p is a prime.
C. H. Li was supported by an Australian Research Council Discovery Grant and a QEII Fellowship. Z. P. Lu was partially supported
by the NNSF and TYYF of China. P. P. Pálfy was supported by the Hungarian Science Foundation (OTKA), grant no. T38059. 相似文献
110.
Yoshimasa Miyata 《Journal of Number Theory》2007,125(2):442-458
Let p be an odd prime number and k a finite extension of Qp. Let K/k be a totally ramified elementary abelian Kummer extension of degree p2 with Galois group G. We determine the isomorphism class of the ring of integers in K as an oG-module under some assumptions. The obtained results imply there exist extensions whose rings are ZpG-isomorphic but not oG-isomorphic, where Zp is the ring of p-adic integers. Moreover we obtain conditions that the rings of integers are free over the associated orders and give extensions whose rings are not free. 相似文献