Banakh, Taras; Lyaskovska, Nadia Weakly P-small not P-small subsets in groups. (English) Zbl 1190.20036 Int. J. Algebra Comput. 18, No. 1, 1-6 (2008). 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. Cited in 5 Documents 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 Keywords:infinite groups; weakly P-small subsets; large subsets; generators Citations:Zbl 1112.20028 × Cite Format Result Cite Review PDF 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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.