# Talk:Subgroup Mapping Matrices (V-maps)/WikispacesArchive

# ARCHIVED WIKISPACES DISCUSSION BELOW

**All discussion below is archived from the Wikispaces export in its original unaltered form.**

Please do not add any new discussion to this archive page.

All new discussion should go on Talk:Subgroup Mapping Matrices (V-maps).

## Abelian groups vs modules

Normally you'd call these abelian groups, or possibly Z-modules, because just calling them modules suggests things which aren't true. I suggest changing this to "abelian groups", which is what it would normally be called and what I've been calling it.

- **genewardsmith** July 31, 2012, 09:09:28 AM UTC-0700

OK, but what's the "dual group" of an abelian group? Is it well-defined?

- **mbattaglia1** July 31, 2012, 09:15:56 AM UTC-0700

And what's the terminology I should use for the fundamental "spaces" in matrices then?

I see there's some precedence for talking about the "column module", "row module", "null module" of an integer matrix acting as a linear transformation on a Z-module, instead of column space, row space, etc. Would I call it the "column group" and "row group"? Would anyone know what I mean?

- **mbattaglia1** July 31, 2012, 09:18:30 AM UTC-0700

Note also I explicitly spelled it out here at the top

http://xenharmonic.wikispaces.com/Temperament+Mapping+Matrices+%28M-maps%29

But I'm curious what things I wrote aren't true of modules in general and only of Z-modules.

- **mbattaglia1** July 31, 2012, 09:26:31 AM UTC-0700