Set Ideals with Isomorphic Symmetry Groups | Zendy

Biryukov Peter | Zendy; Mishkin Valery | Zendy

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Set Ideals with Isomorphic Symmetry Groups

Author(s) -

Biryukov Peter,

Mishkin Valery

Publication year - 2002

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609301008724

Subject(s) - mathematics , ideal (ethics) , pure mathematics , isomorphism (crystallography) , symmetry (geometry) , order (exchange) , group (periodic table) , set (abstract data type) , class (philosophy) , quotient , separable space , automorphism group , automorphism , mathematical analysis , geometry , philosophy , chemistry , organic chemistry , epistemology , finance , artificial intelligence , computer science , crystal structure , programming language , economics , crystallography

A criterion of isomorphism for symmetry groups of set ideals is provided in terms of ideal quotients and cardinal invariants. Furthermore, set ideals with complete symmetry group are characterized. They form a wide class, comprising, for example, all uniform dense ideals and the ideals of ‘thin’ sets in separable metric spaces. If the symmetry group of a set ideal is not complete, then its outer automorphism group is shown to be cyclic of order 2. 2000 Mathematics Subject Classification 20B35, 20B27, 03E50, 04A20.

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