caa a22 4500 465743625 CHVBK 20180323111814.0 cr unu---uuuuu 170327e19900501xx s 000 0 eng 10.1007/BF01621468 doi (NATIONALLICENCE)springer-10.1007/BF01621468 Brendle Jörg Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, W-7400, Tübingen, Federal Republic of Germany aut Cardinal invariants of infinite groups [Elektronische Daten] [Jörg Brendle] LetG be a group. CallG akC-group if every element ofG has less thank conjugates. Denote byP(G) the least cardinalk such that any subset ofG of sizek contains two elements which commute. It is shown that the existence of groupsG such thatP(G) is a singular cardinal is consistent withZFC. So is the existence of groupsG which are notkC but haveP(G)<k wherek is a limit cardinal. On the other hand, ifk is a singular strong limit cardinal, andG is akC-group, thenP(G)≠k. This partially answers questions, and improves results, of Faber, Laver and McKenzie. Springer-Verlag, 1990 Archive for Mathematical Logic Springer-Verlag 30/3(1990-05-01), 155-170 0933-5846 30:3<155 1990 30 153 https://doi.org/10.1007/BF01621468 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01621468 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Brendle Jörg Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, W-7400, Tübingen, Federal Republic of Germany aut NATIONALLICENCE 773 0- Archive for Mathematical Logic Springer-Verlag 30/3(1990-05-01), 155-170 0933-5846 30:3<155 1990 30 153 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer