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[reply]

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

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)[reply]

@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)[reply]

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.^[1] 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)[reply]

Thank you, Lambiam. I hope Wlod will come here soon to see your answer.

CiaPan (talk) 11:21, 23 February 2021 (UTC)[reply]