Name
Abstract | ||
|---|---|---|
We prove that for every k is an element of N, each countable infinite group G admits a partition G = A boolean OR B into two sets which are k-meager in the sense that for every k-element subset K subset of G the sets K A and K B are not thick. The proof is based on the fact that G possesses a syndetic submeasure, i.e. a left-invariant submeasure mu : P(G) -> [0, 1] such that for each epsilon > 1/vertical bar G vertical bar and subset A subset of G with mu(A) < 1 there is a set B subset of G\A such that mu(B) < epsilon and F B = G for some finite subset F subset of G. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1142/S0218196713500392 | INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION |
Keywords | Field | DocType |
Syndetic submeasure, amenable group, minimal action, thick subset | Discrete mathematics,Amenable group,Combinatorics,Infinite group,Countable set,Partition (number theory),Mathematics | Journal |
Volume | Issue | ISSN |
23 | 7 | 0218-1967 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Taras O. Banakh | 1 | 9 | 7.24 |
| Igor Protasov | 2 | 0 | 2.70 |
| Sergiy Slobodianiuk | 3 | 0 | 1.01 |