Definition talk:Normal Subgroup

I think there should be a separation between the many forms that fall under "subgroup and normal subset" and the one (presently) that does not. --Dfeuer (talk) 13:30, 3 February 2013 (UTC)

That is, definitions 1,3,4,5,and 6 all fall under definition 7. As noted on the page defining normal subset, there's another pair of forms remaining to that (that I can think of right now). There's also a form "xy \in N \implies yx \in N" on that page and not this. I'd love to reduce the clutter on the main transcluding page and make room for other ideas, in particular "normal subgroup iff kernel of a homomorphism". --Dfeuer (talk) 13:34, 3 February 2013 (UTC)


 * I don't agree. Please leave as it is. The definitions for normal subgroups are defined as they are in the context of subgroups. Many accounts of group theory don't bother with the concept of "normal subset" so we should provide the complete gamut of definitions of normal subgroup without reference to normal subset. --prime mover (talk) 13:41, 3 February 2013 (UTC)


 * "normal subgroup iff kernel of a homomorphism" is already covered. It does not need to go into "definitions" unless you can cite a specific reference that defines a normal subgroup in such a way. --prime mover (talk) 13:43, 3 February 2013 (UTC)


 * In response to the philosophy that you espouse: yes, you can derive all sorts of equivalences for a normal subgroup and normal subset and so on, but unless such definitions are actually used in texts as the basis of an exposition, I would argue that they do not get included in the definitions page. It's unwieldy enough as it is. --prime mover (talk) 13:46, 3 February 2013 (UTC)


 * I don't see why the umbrella of equivalent definitions shouldn't expand enough to cover all the various equivalence theorems. I'm not suggesting that the various forms of "subgroup and normal subset" be removed, but that they be visually grouped together rather than mixed in with the more significantly different definitions. --Dfeuer (talk) 14:32, 3 February 2013 (UTC)


 * The current way it's strtuctured it would be a major pain in the neck to maintain. Can't you just leave it be? --prime mover (talk) 14:34, 3 February 2013 (UTC)

Lost notation
When you deleted some things from the end of the page, it seems that a bit of alternative notation may have gone missing. Dfeuer (talk) 14:37, 3 February 2013 (UTC)


 * No, I moved it. --prime mover (talk) 14:56, 3 February 2013 (UTC)


 * You may be right - what specifically is missing? --prime mover (talk) 15:38, 3 February 2013 (UTC)


 * It looked something like $N^g$, I think. I don't remember exactly. --Dfeuer (talk) 15:44, 3 February 2013 (UTC)


 * I also don't remember what it meant. --Dfeuer (talk) 15:46, 3 February 2013 (UTC)


 * Moved to Definition:Normal Subgroup/Definition 5 where it was directly relevant. --prime mover (talk) 16:02, 3 February 2013 (UTC)