On subgroups in the group of limited permutations

N. Suchkov,   N. Suchkova

A permutation \(g\) of a nonempty set \(M\) of numbers is said to be limited if \[w(g)= \max_{\alpha\in M}{|\alpha-\alpha^g|}<\infty.\] Clearly, all limited permutations of \(M\) form a group. The groups \(F\) and \(H\) of all limited permutations of the sets of integers \(Z\) and naturals \(N\) were studied in [1-3].

Theorem. The locally finite radicals of the groups \(F\) and \(H\) have cardinality continuum.

References

1. N. M. Suchkov, An example of a mixed group factorized by two periodic subgroups, Algebra and logic, 23, N5 (1984), 573–577.
2. N. M. Suchkov, On subgroups of the product of locally finite groups, Algebra and logic, 24, N4 (1985), 408–413.
3. N. M. Suchkov, N. G. Suchkova, On groups of limited permutations, J. Sib. Federal Univ., Math. and Phys., 3, N2 (2010), 262–266.

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