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Weakly P-small not P-small subsets in groups. (English) Zbl 1190.20036

Summary: Answering a question of D. Dikranjan and I. Protasov [Appl. Gen. Topol. 7, No. 2, 265-268 (2006; Zbl 1112.20028)] we prove that each infinite group \(G\) contains a weakly P-small subset \(A\subset G\) which is not P-small. This means that for every \(n\) there are \(n\) pairwise disjoint translation copies of \(A\) in \(G\) but there are not infinitely many such disjoint copies.

MSC:

20F99 Special aspects of infinite or finite groups
20F05 Generators, relations, and presentations of groups
22A05 Structure of general topological groups
54H11 Topological groups (topological aspects)
22D05 General properties and structure of locally compact groups

Citations:

Zbl 1112.20028
Full Text: DOI

References:

[1] Banakh T., Algebra Discrete Math. 3 pp 29–
[2] DOI: 10.1007/978-3-642-65780-1 · doi:10.1007/978-3-642-65780-1
[3] DOI: 10.4995/agt.2006.1929 · Zbl 1112.20028 · doi:10.4995/agt.2006.1929
[4] Hidman N., de Gruyter Exposition in Mathematics 27, in: Theory and Applications (1998)
[5] Protasov I., Monograph Series 2, in: Combinatorics of Numbers (1997)
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