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Article #108Complete Groups / S_6
From: Jack McKinney
Date: Mon, 28 Sep 1992 20:12
Date: Mon, 28 Sep 1992 20:12
13 lines
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1409 bytes
A complete group is one that is isomorphic to its group of Automorphisms. The symmetric group on n elements is complete for all integers n _except_ 2 and 6. It is also true that the outer automorphisms of S_6 form one coset to the set of inner automorphisms. Can someone provide an outer automorphism on S_6 ? (This would completely specify Aut(S_6), which is isomorphic to S_6 x Z_2) +-----------------------------------------------+-------------------------+ | "A container of ashes might one day be thrown | Jack McKinney | | from the sky, which could burn the land and | jmckinney@tamu.edu | | boil the oceans." +-------------------------+ | -From the Hopi prophecy | Koyaanisqatsi | +-----------------------------------------------+-------------------------+
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<1992Sep28.201204.13907@tamsun.tamu.edu>Path:
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Newsgroups: sci.math.research Path: arc1-ca.pugleaf.net!sparky!uunet!think.com!wupost!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet From: rlm7638@tamsun.tamu.edu (Jack McKinney) Subject: Complete Groups / S_6 Message-ID: <1992Sep28.201204.13907@tamsun.tamu.edu> Sender: Daniel Grayson <dan@math.uiuc.edu> X-Submissions-To: sci-math-research@uiuc.edu Organization: Texas A&M University, College Station X-Administrivia-To: sci-math-research-request@uiuc.edu Approved: Daniel Grayson <dan@math.uiuc.edu> Date: Mon, 28 Sep 1992 20:12:57 GMT Lines: 14