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	<updated>2026-06-29T01:24:16Z</updated>
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	<entry>
		<id>https://en.xen.wiki/index.php?title=Talk:Subgroup_basis_matrix/WikispacesArchive&amp;diff=128143&amp;oldid=prev</id>
		<title>FloraC: FloraC moved page Talk:Subgroup basis matrices/WikispacesArchive to Talk:Subgroup basis matrix/WikispacesArchive: WP:PLURAL</title>
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		<updated>2023-11-27T15:48:24Z</updated>

		<summary type="html">&lt;p&gt;FloraC moved page &lt;a href=&quot;/w/Talk:Subgroup_basis_matrices/WikispacesArchive&quot; class=&quot;mw-redirect&quot; title=&quot;Talk:Subgroup basis matrices/WikispacesArchive&quot;&gt;Talk:Subgroup basis matrices/WikispacesArchive&lt;/a&gt; to &lt;a href=&quot;/w/Talk:Subgroup_basis_matrix/WikispacesArchive&quot; title=&quot;Talk:Subgroup basis matrix/WikispacesArchive&quot;&gt;Talk:Subgroup basis matrix/WikispacesArchive&lt;/a&gt;: WP:PLURAL&lt;/p&gt;
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				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 15:48, 27 November 2023&lt;/td&gt;
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&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>FloraC</name></author>
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		<id>https://en.xen.wiki/index.php?title=Talk:Subgroup_basis_matrix/WikispacesArchive&amp;diff=81109&amp;oldid=prev</id>
		<title>FloraC: FloraC moved page Talk:Subgroup Basis Matrices/WikispacesArchive to Talk:Subgroup basis matrices/WikispacesArchive: WP:NCCAPS</title>
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		<updated>2021-11-19T22:52:15Z</updated>

		<summary type="html">&lt;p&gt;FloraC moved page &lt;a href=&quot;/w/Talk:Subgroup_Basis_Matrices/WikispacesArchive&quot; class=&quot;mw-redirect&quot; title=&quot;Talk:Subgroup Basis Matrices/WikispacesArchive&quot;&gt;Talk:Subgroup Basis Matrices/WikispacesArchive&lt;/a&gt; to &lt;a href=&quot;/w/Talk:Subgroup_basis_matrices/WikispacesArchive&quot; class=&quot;mw-redirect&quot; title=&quot;Talk:Subgroup basis matrices/WikispacesArchive&quot;&gt;Talk:Subgroup basis matrices/WikispacesArchive&lt;/a&gt;: WP:NCCAPS&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 22:52, 19 November 2021&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-notice&quot; lang=&quot;en&quot;&gt;&lt;div class=&quot;mw-diff-empty&quot;&gt;(No difference)&lt;/div&gt;
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		<author><name>FloraC</name></author>
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	<entry>
		<id>https://en.xen.wiki/index.php?title=Talk:Subgroup_basis_matrix/WikispacesArchive&amp;diff=68842&amp;oldid=prev</id>
		<title>Mike Battaglia: Mike Battaglia moved page Talk:Subgroup Mapping Matrices (V-maps)/WikispacesArchive to Talk:Subgroup Basis Matrices/WikispacesArchive: Clarify terminology; &quot;subgroup mapping&quot; sounds like a mapping matrix *on* a subgroup</title>
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		<updated>2021-04-26T19:16:19Z</updated>

		<summary type="html">&lt;p&gt;Mike Battaglia moved page &lt;a href=&quot;/w/Talk:Subgroup_Mapping_Matrices_(V-maps)/WikispacesArchive&quot; class=&quot;mw-redirect&quot; title=&quot;Talk:Subgroup Mapping Matrices (V-maps)/WikispacesArchive&quot;&gt;Talk:Subgroup Mapping Matrices (V-maps)/WikispacesArchive&lt;/a&gt; to &lt;a href=&quot;/w/Talk:Subgroup_Basis_Matrices/WikispacesArchive&quot; class=&quot;mw-redirect&quot; title=&quot;Talk:Subgroup Basis Matrices/WikispacesArchive&quot;&gt;Talk:Subgroup Basis Matrices/WikispacesArchive&lt;/a&gt;: Clarify terminology; &amp;quot;subgroup mapping&amp;quot; sounds like a mapping matrix *on* a subgroup&lt;/p&gt;
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				&lt;td colspan=&quot;1&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 19:16, 26 April 2021&lt;/td&gt;
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&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>Mike Battaglia</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Talk:Subgroup_basis_matrix/WikispacesArchive&amp;diff=34954&amp;oldid=prev</id>
		<title>Mike Battaglia: 1 revision imported: Moving archived Wikispaces discussion to subpage</title>
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		<updated>2018-10-01T18:01:48Z</updated>

		<summary type="html">&lt;p&gt;1 revision imported: Moving archived Wikispaces discussion to subpage&lt;/p&gt;
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&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;</summary>
		<author><name>Mike Battaglia</name></author>
	</entry>
	<entry>
		<id>https://en.xen.wiki/index.php?title=Talk:Subgroup_basis_matrix/WikispacesArchive&amp;diff=34953&amp;oldid=prev</id>
		<title>Wikispaces&gt;FREEZE at 18:01, 1 October 2018</title>
		<link rel="alternate" type="text/html" href="https://en.xen.wiki/index.php?title=Talk:Subgroup_basis_matrix/WikispacesArchive&amp;diff=34953&amp;oldid=prev"/>
		<updated>2018-10-01T18:01:16Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{WSArchiveHeader}}&lt;br /&gt;
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== Abelian groups vs modules ==&lt;br /&gt;
Normally you&amp;#039;d call these abelian groups, or possibly Z-modules, because just calling them modules suggests things which aren&amp;#039;t true. I suggest changing this to &amp;quot;abelian groups&amp;quot;, which is what it would normally be called and what I&amp;#039;ve been calling it.&lt;br /&gt;
&lt;br /&gt;
- &amp;#039;&amp;#039;&amp;#039;genewardsmith&amp;#039;&amp;#039;&amp;#039; July 31, 2012, 09:09:28 AM UTC-0700&lt;br /&gt;
----&lt;br /&gt;
OK, but what&amp;#039;s the &amp;quot;dual group&amp;quot; of an abelian group? Is it well-defined?&lt;br /&gt;
&lt;br /&gt;
- &amp;#039;&amp;#039;&amp;#039;mbattaglia1&amp;#039;&amp;#039;&amp;#039; July 31, 2012, 09:15:56 AM UTC-0700&lt;br /&gt;
----&lt;br /&gt;
And what&amp;#039;s the terminology I should use for the fundamental &amp;quot;spaces&amp;quot; in matrices then?&lt;br /&gt;
&lt;br /&gt;
I see there&amp;#039;s some precedence for talking about the &amp;quot;column module&amp;quot;, &amp;quot;row module&amp;quot;, &amp;quot;null module&amp;quot; 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 &amp;quot;column group&amp;quot; and &amp;quot;row group&amp;quot;? Would anyone know what I mean?&lt;br /&gt;
&lt;br /&gt;
- &amp;#039;&amp;#039;&amp;#039;mbattaglia1&amp;#039;&amp;#039;&amp;#039; July 31, 2012, 09:18:30 AM UTC-0700&lt;br /&gt;
----&lt;br /&gt;
Note also I explicitly spelled it out here at the top&lt;br /&gt;
&lt;br /&gt;
http://xenharmonic.wikispaces.com/Temperament+Mapping+Matrices+%28M-maps%29&lt;br /&gt;
&lt;br /&gt;
But I&amp;#039;m curious what things I wrote aren&amp;#039;t true of modules in general and only of Z-modules.&lt;br /&gt;
&lt;br /&gt;
- &amp;#039;&amp;#039;&amp;#039;mbattaglia1&amp;#039;&amp;#039;&amp;#039; July 31, 2012, 09:26:31 AM UTC-0700&lt;br /&gt;
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		<author><name>Wikispaces&gt;FREEZE</name></author>
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