https://groupprops.subwiki.org/w/index.php?action=history&feed=atom&title=Join-transiterJoin-transiter - Revision history2026-04-26T06:47:14ZRevision history for this page on the wikiMediaWiki 1.41.2https://groupprops.subwiki.org/w/index.php?title=Join-transiter&diff=6192&oldid=prevVipul: 1 revision2008-05-07T23:45:53Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://groupprops.subwiki.org/w/index.php?title=Join-transiter&diff=6191&oldid=prevVipul at 17:05, 15 March 20072007-03-15T17:05:01Z<p></p>
<p><b>New page</b></p><div>{{subgroup property modifier}}<br />
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{{transiter}}<br />
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==Definition==<br />
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===Symbol-free definition===<br />
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Let <math>p</math> be a [[subgroup property]]. Then the '''join-transiter''' of <math>p</math> is the property of being a subgroup such that its join with any subgroup having property <math>p</math> again has property <math>p</math> in the whole group.<br />
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===Definition with symbols===<br />
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Let <math>p</math> be a [[subgroup property]]. Then the join-transiter of <math>p</math> is the property <math>q</math> such that: A subgroup <math>H</math> has property <math>q</math> in <math>G</math> if and only if whenever <math>K \le G</math> has property <math>p</math>, <math><H,K></math> has property <math>p</math> in <math>G</math>.</div>Vipul