Talk:Slender group

What is Q?

The Examples section requires a lot more explanation. Specifically, there's no indication of what Q is supposed to mean.

166.137.101.169 (talk) 23:07, 25 June 2014 (UTC)Collin237

It is the additive group of rational numbers: added now. Deltahedron (talk) 18:35, 26 June 2014 (UTC)

Were slender groups introduced by Jerzy Łoś (one of the two co-inventors of the ultra-filter)?

Can one check this info?

Before the homological algebra took over, Jerzy Łoś was a pioneer of infinite torsion-free abelian groups; he had involved his students, including Andrzej Ehrenfeucht. — Preceding unsigned comment added by Wlod (talk • contribs) 04:18, 29 April 2018 (UTC)

@Wlod: R. J. Nunke in "Slender groups" (referenced in our article, available here https://www.ams.org/journals/bull/1961-67-03/S0002-9904-1961-10582-X/home.html with a full-text PDF file freely downloadable) says

Łoś calls a torsion-free abelian group A slender if every homomorphism of P into A sends all but a finite number of the 5n into 0. The concept first appeared in [3]. (...)

and [3] is L. Fuchs, Abelian groups, Budapest, Publishing House of the Hungarian Academy of Sciences, 1958.

If I understand it correctly, this means J.Łoś gave a name to a notion devised by László Fuchs. --CiaPan (talk) 08:49, 23 February 2021 (UTC)

In the third edition of his Abelian Groups (1960), when introducing the notion of a slender group, Fuchs writes in a footnote: This notion is due to Łoś. Prof. J. Łoś has kindly permitted to make use of his results on slender groups before their publication by him. So while its first appearance is in this book, the notion appears to have not only been named but also devised by Jerzy Łoś – at least, that is how I interpret "This notion is due to".  --Lambiam 11:08, 23 February 2021 (UTC)

Thank you, Lambiam. I hope Wlod will come here soon to see your answer. CiaPan (talk) 11:21, 23 February 2021 (UTC)