https://groupprops.subwiki.org/w/index.php?action=history&feed=atom&title=Normal_not_implies_subgroup-conjugating 2026-08-02T00:23:41Z Revision history for this page on the wiki MediaWiki 1.41.2 https://groupprops.subwiki.org/w/index.php?title=Normal_not_implies_subgroup-conjugating&diff=12662&oldid=prev 2008-09-05T11:30:46Z

<p>New page: {{automorphism property non-implication| stronger = normal automorphism| weaker = subgroup-conjugating automorphism}} ==Statement== A <a href="/wiki/Normal_automorphism" title="Normal automorphism">normal automorphism</a> of a group (an automorphism ...</p> <p><b>New page</b></p><div>{{automorphism property non-implication|<br /> stronger = normal automorphism|<br /> weaker = subgroup-conjugating automorphism}}<br /> <br /> ==Statement==<br /> <br /> A [[normal automorphism]] of a group (an automorphism that preserves all the normal subgroups) need not be [[subgroup-conjugating automorphism|subgroup-conjugating]] -- it need not send every subgroup to a conjugate subgroup.<br /> <br /> ==Related facts==<br /> <br /> ===Stronger facts===<br /> <br /> * [[Class-preserving not implies subgroup-conjugating]]: An automorphism of a group that preserves conjugacy classes of elements need not send every subgroup to a conjugate subgroup.<br /> <br /> ==Facts used==<br /> # [[Class-preserving not implies subgroup-conjugating]]<br /> # [[Class-preserving implies normal]]<br /> <br /> ==Proof==<br /> <br /> The proof follows directly by piecing together facts (1) and (2).</div>

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