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Titlebook: Ordered Groups and Infinite Permutation Groups; W. Charles Holland Book 19961st edition Kluwer Academic Publishers 1996 automorphism.group

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書目名稱Ordered Groups and Infinite Permutation Groups
編輯W. Charles Holland
視頻videohttp://file.papertrans.cn/704/703645/703645.mp4
叢書名稱Mathematics and Its Applications
圖書封面Titlebook: Ordered Groups and Infinite Permutation Groups;  W. Charles Holland Book 19961st edition Kluwer Academic Publishers 1996 automorphism.group
描述The subjects of ordered groups and of infinite permutation groups have long en- joyed a symbiotic relationship. Although the two subjects come from very different sources, they have in certain ways come together, and each has derived considerable benefit from the other. My own personal contact with this interaction began in 1961. I had done Ph. D. work on sequence convergence in totally ordered groups under the direction of Paul Conrad. In the process, I had encountered "pseudo-convergent" sequences in an ordered group G, which are like Cauchy sequences, except that the differences be- tween terms of large index approach not 0 but a convex subgroup G of G. If G is normal, then such sequences are conveniently described as Cauchy sequences in the quotient ordered group GIG. If G is not normal, of course GIG has no group structure, though it is still a totally ordered set. The best that can be said is that the elements of G permute GIG in an order-preserving fashion. In independent investigations around that time, both P. Conrad and P. Cohn had showed that a group admits a total right ordering if and only if the group is a group of automor- phisms of a totally ordered set. (In a right
出版日期Book 19961st edition
關(guān)鍵詞automorphism; group action; Lattice
版次1
doihttps://doi.org/10.1007/978-1-4613-3443-9
isbn_softcover978-1-4613-3445-3
isbn_ebook978-1-4613-3443-9
copyrightKluwer Academic Publishers 1996
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Locally Moving Groups and Reconstruction Problems,such a reconstruction theorem for a certain class of locally compact topological spaces. Then we prove a reconstruction theorem for subspaces of the foliated torus. In Section 4 we present a reconstruction theorem for 2-homogeneous linear orders and circular orders.
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Mathematics and Its Applicationshttp://image.papertrans.cn/o/image/703645.jpg
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https://doi.org/10.1007/978-1-4613-3443-9automorphism; group action; Lattice
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Permutation Groups Whose Subgroups Have Just Finitely Many Orbits,In this note we answer a question of Peter Neumann, based on some earlier more general questions of R. Zimmer concerning actions of arithmetic groups and Lie groups on manifolds. The main question of Zimmer is the following.
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978-1-4613-3445-3Kluwer Academic Publishers 1996
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