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The number of non-solutions of an equation in a group
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Anton A. Klyachko
Published/Copyright:
November 18, 2005
Abstract
It is shown that, for any pair of cardinals with infinite sum, there exist a group and an equation over this group such that the first cardinal is the number of solutions to this equation and the second cardinal is the number of non-solutions. A countable torsion-free nontopologizable group is constructed.
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Published Online: 2005-11-18
Published in Print: 2005-11-18
Walter de Gruyter GmbH & Co. KG
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Articles in the same Issue
- Elements of order at most 4 in finite 2-groups, 2
- On the number of infinite branches in the graph of all p-groups of coclass r
- Polynomial properties in unitriangular matrices. II
- Connectivity of the coset poset and the subgroup poset of a group
- The number of non-solutions of an equation in a group
- Groups, periodic planes and hyperbolic buildings
- Endomorphisms preserving an orbit in a relatively free metabelian group
- Generic units in abelian group rings
- Subgroup growth of Baumslag–Solitar groups
