# Meaning of “Komplex” (mathematical context)

I am currently struggling to understand the article “Zur Theorie der faktorisierbaren Gruppen”, by L. Redei in Acta Math. Acad. Sci. Hung. 1, 74--98 (1950).

As might be expected, there are several specialized German mathematical words that an ordinary dictionary fails to contain.

In particular I'm struggling with the word “Komplex”. In following the paragraph introducing the word “Komplex”, followed by my dubious translation.

Original:

Bezeichne H eine beliebig vorgelegte Gruppe. Für gewöhnlich versteht man unter einem Komplex K (von H) eine Teilmenge von H, oft kommt es aber auch vor, daß man dabei den Elementen des Komplexes eine Multiplizität zukommen läßt. Das wollen wir tun, so daß einen Komplex in der Form K=a1γ1,a2γ2, … annehmen, wobei γ123…, alle verschiedenen Elementen von H sind und jedes ai gleich 0,1,2 …∞ ist.

My translation:

Let H be any finite group. What we mean by a complex K (of H) is usually a subset of H, but where we allow the elements of the complex to have multiplicities. So we will write a complex in the form K=a1γ1,a2γ2, …, where γ123… are all different elements of H and each ai is one of 0,1,2 …∞.

• I think you should ask in the chat of Mathematica.SE for German-speaking Mathematicians helping you here. Nov 22, 2012 at 20:40
• I think you mean chat.stackexchange.com/rooms/36 - this is a math question, not a Mathematica question. Nov 25, 2012 at 12:57
• "... eine beliebig vergelegte Gruppe" is wrong. I think it's a typo but not sure what it should be. vorgelegt, perhaps?
– Em1
Nov 26, 2012 at 13:25
• @Em1 : about "vergelegte" it’s a messy photocopy and I hesitated between "vOrgelegte" and "vErgelegte". In any case, I did not find it in the dictionary and my translation is pure guesswork Nov 26, 2012 at 13:41
• Ewan, I see, you cannot go to the chat. You must register first, I guess. And for sure you need a reputation score of 20 … sad that. I’m not a mathematician, so I cannot help here, but a special math dictionary should help you: google.com/… Nov 26, 2012 at 18:23

If I am not mistaken, `Komplex` is the short form for Kettenkomplex, so the proper English word is chain complex. https://en.wikipedia.org/wiki/Chain_complex
`Komplex` means `Subset of a semigroup`, see e.g. Specht, "Die Untergruppen einer Gruppe", Springer 1956. Note that in contrast to a `subgroup`, a Komplex need not be a group (or even a semigroup) itself. I am not aware of an English translation, so you're free to invent one yourself. I should add that until now, I did not come across the term, and as far as I can see, it has been out of fashion for quite some time.