Talk:Properties of Relation Compatible with Group Operation

Reorganize
I've based my work in this area primarily on what I found in Properties of Ordered Ring. However, as I've worked with the material, I've come to realize that some of these properties are trivial special cases of other properties that are just as easy to understand and prove. Here's the breakdown, as I see it, freely mixing :


 * Properties of Relation Compatible with Group Operation/CRG1 -- primary
 * Properties of Relation Compatible with Group Operation/CRG2 -- secondary to CRG1
 * Properties of Relation Compatible with Group Operation/CRG3 (not in the original PoOR) -- primary
 * Properties of Relation Compatible with Group Operation/CRG4 -- secondary to CRG3
 * Operating on Transitive Relationships Compatible with Operation (not in the original PoOR) -- primary


 * Transitive Relation Compatible with Semigroup Operation Relates Powers of Related Elements (not in the original PoOR)-- an easy but useful consequence of Operating on Transitive Relationships Compatible with Operation
 * User:Dfeuer/CTR5 -- secondary to Transitive Relation Compatible with Semigroup Operation Relates Powers of Related Elements

I'd like very much to reorder/rearrange these things somewhat so as to gather the most general forms together in one place, while also keeping the special cases accessible. Any constructive thoughts on how to accomplish this? --Dfeuer (talk) 23:03, 26 January 2013 (UTC)


 * The word "Corollary" comes to mind. --Lord_Farin (talk) 23:07, 26 January 2013 (UTC)


 * Are this page and User:Dfeuer/Properties of Ordered Group shaping up as you think they should? --Dfeuer (talk) 23:46, 26 January 2013 (UTC)


 * Disregarding the still persistent problems with naming, they are, superficially. It would however be advisable to have the corollaries included on the actual subpages (such as CRG2 appearing as a corollary on CRG1). In general, the structure is like for Ring Homomorphism Preserves Subrings and its corollary, with the same naming conventions. Deviations on this are up to now only present - or so I think - when the corollary is a named theorem in itself, in which case the stronger theorem should be referred to in the "Also see" section. As such does not apply I will refrain from further details on how I would handle that case; I hope this will appear in due time in the Help section of the site. --Lord_Farin (talk) 15:05, 27 January 2013 (UTC)


 * That looks easy enough to arrange. Since I'd like very much to push the ordered groups stuff to main today, do you think you could either come up with better names or give your blessing to use these awful ones temporarily? As for the "/corollary" convention, I don't quite see the point—why not describe the corollary itself to make it easy to find if you don't know what it's a corollary of? --Dfeuer (talk) 17:58, 27 January 2013 (UTC)


 * I spoke too fast. Several of the theorems on ordered groups are (intentionally) corollaries of theorems on relations compatible with a group operation and also corollaries of other theorems on ordered groups. If we name them "blah/corollary", which blah do we choose?


 * Hm, I thought I had said something about that case as well. I meant to have said that in that case, the corollary should have its own page. In general, the corollaries are minor results suffering from the same naming problems recurring over and over again. This approach relieves a bit the need for good names. --Lord_Farin (talk) 09:43, 28 January 2013 (UTC)

Darn. There goes that idea. --Dfeuer (talk) 14:27, 28 January 2013 (UTC)