Talk:Direct product of groups

fibre product

--Lendormi (talk) 11:28, 13 January 2012 (UTC)

In the section Fiber product, I don't see any reason to require that the morphisms are epimorphisms.

Wikimarkup versus explicit HTML for list markup

There's an edit war about the right way to format certain parts of the article, specifically whether wikimarkup or explicit HTML must be used. The article contains several sections where to the best of my knowledge the intended and correct indentation cannot be created using wikimarkup alone. Examples (from section, well, "Examples"):

First with wikimarkup alone:

• Let R be the group of real numbers under addition. Then the direct product R × R is the group of all two-component vectors (x, y) under the operation of vector addition:

(x₁, y₁) + (x₂, y₂)  =  (x₁ + x₂, y₁ + y₂).

• Let G and H be cyclic groups with two elements each:

G ∙ 1 a 1 1 a a a 1

H ∙ 1 b 1 1 b b b 1

Then the direct product G × H is isomorphic to the Klein four-group:

G × H

∙	(1, 1)	(a, 1)	(1, b)	(a, b)
(1, 1)	(1, 1)	(a, 1)	(1, b)	(a, b)
(a, 1)	(a, 1)	(1, 1)	(a, b)	(1, b)
(1, b)	(1, b)	(a, b)	(1, 1)	(a, 1)
(a, b)	(a, b)	(1, b)	(a, 1)	(1, 1)

This is supposed to be a two-element unordered list. However, the second list entry is broken semantically and visually as the tables are not interpreted as part of the list entry, and their indentation is wrong. Now using HTML:

• Let R be the group of real numbers under addition. Then the direct product R × R is the group of all two-component vectors (x, y) under the operation of vector addition:

  (x₁, y₁) + (x₂, y₂)  =  (x₁ + x₂, y₁ + y₂).

• Let G and H be cyclic groups with two elements each:

  G ∙ 1 a 1 1 a a a 1

  H ∙ 1 b 1 1 b b b 1

  Then the direct product G × H is isomorphic to the Klein four-group:

  G × H

  ∙	(1, 1)	(a, 1)	(1, b)	(a, b)
  (1, 1)	(1, 1)	(a, 1)	(1, b)	(a, b)
  (a, 1)	(a, 1)	(1, 1)	(a, b)	(1, b)
  (1, b)	(1, b)	(a, b)	(1, 1)	(a, 1)
  (a, b)	(a, b)	(1, b)	(a, 1)	(1, 1)

Here the indentation of the tables is correct, and the second list entry is not broken. I don't see how this can be accomplished using wikimarkup alone, and Help:List appears to agree, as far as I can see. – Tea2min (talk) 11:22, 1 June 2016 (UTC)

How about this -- no div-style, and just plain wiki markup:

• Let G and H be cyclic groups with two elements each:

G ∙ 1 a 1 1 a a a 1

H ∙ 1 b 1 1 b b b 1

Then the direct product G × H is isomorphic to the Klein four-group:

And so on. Its wikimarkup, but I just put a single colon in front of the table to indent it. No raw html markup. 14:29, 3 August 2016 (UTC)

Proposed merge

The proposal is to merge Direct sum of groups into Direct product of groups.

The article Direct sum of groups is describing the same construction as Direct product of groups. There is a difference in the case of infinite direct sums, but in the literature those are almost always in the setting of infinite direct sums of abelian groups (or vector spaces or modules), and those are amply described already at articles such as Direct sum and Direct sum of modules. See WP:CONTENTFORK. —Ebony Jackson (talk) 20:36, 27 February 2026 (UTC)