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- Title
A nonstandard construction of direct limit group actions.
- Authors
TAKUMA IMAMURA
- Abstract
Manevitz and Weinberger (1996) proved that the existence of effective K- Lipschitz Z/nZ-actions implies the existence of effective K-Lipschitz Q/Z-actions for all compact connected manifolds with metrics, where K is a fixed Lipschitz constant. The Q=Z-actions were constructed from suitable actions of a suffciently large hyper-finite cyclic group Z/Z in the sense of nonstandard analysis. By modifying their construction, we prove that for every direct system of torsion groups with monomorphisms, the existence of effective K-Lipschitz actions implies the existence of effective K-Lipschitz lim G-actions. This generalises Manevitz and Weinberger's result.
- Subjects
NONSTANDARD mathematical analysis; CYCLIC groups; FINITE groups; TORSION
- Publication
Mathematical Communications, 2022, Vol 27, Issue 1, p63
- ISSN
1331-0623
- Publication type
Article