Isometry Dimension of Finite Groups
نویسندگان
چکیده
منابع مشابه
The Isometry Dimension and Orbit Number of a Finite Group
A finite set W ⊂ R is said to realize the group G if the isometry group of W is isomorphic to G. The isometry dimension of a group is the minimum dimension of a realization. It is known that the isometry dimension of G is less than |G| [1]. We show that the isometry dimension of Z2 is n. The orbit number of a group is the minimum number of orbits in a realization. We show that the groups Z2 are...
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The Morley rank is the usual notion of dimension in model theory which encapsulates the more classical notion of dimension of algebraic varieties in algebraic geometry. In this paper we give a survey of results concerning the classification of infinite simple groups of finite Morley rank. We emphasize both the developments parallel to the Classification of the Finite Simple Groups and the incre...
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Two isometry groups of combinatorial codes are described: the group of automorphisms and the group of monomial automorphisms, which is the group of those automorphisms that extend to monomial maps. Unlike the case of classical linear codes, where these groups are the same, it is shown that for combinatorial codes the groups can be arbitrary different. Particularly, there exist codes with the fu...
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Let X be a proper CAT(0)-space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is non-elementary and contains a rank-one element then its second bounded cohomology group with coefficients in the regular representation is non-trivial. As a consequence, up to passing to an open subgroup of finite index, either G is a compact extension of a totally disconnected ...
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When C ⊆ F is a linear code over a finite field F, every linear Hamming isometry of C to itself is the restriction of a linear Hamming isometry of F to itself, i.e., a monomial transformation. This is no longer the case for additive codes over non-prime fields. Every monomial transformation mapping C to itself is an additive Hamming isometry, but there exist additive Hamming isometries that are...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8973