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Schur multipliers of alternating groups are calculated in
Aschbacher's text on Finite Groups. In particular it contains the following two lemmas: The exponent of the Schur multiplier divides the order of the finite group. If a Sylow subgroup of the group is cyclic, then the corresponding Sylow of
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I have checked out
Karpinsky's book 'The Schur Multiplier' but have to return it Monday. I am making notes on his construction of central extensions of symmetric and alternating groups. I will see whether I can describe them clearly in a way that will fit into this article.
684:
I would add the data on the conjugacy classes to the French article. These data are easy to prove, but I don't find them in my textbooks and I would like to give a reference. Can anybody indicate a reference ? (A source in
English is good, of course.) Thanks.
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Since SL(2,3) is a stem extension of PSL(2,3)=A4, and the Schur multiplier of C2 x C2 is C2, the Schur multiplier of A4 is C2. One could also just work out the homology, the cohomology, and the Hopf formula by hand for A1=A2=1, A3=C3, and A4.
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I have trouble believing that PSL(2,F_4) is isomorphic to PSL(2,F_5), because I think the size of PSL(2,F_q) depends in a simple way on q that rules this out. But I'm very jetlagged right now so maybe I'm mixed up! Can anyone clear this up?
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The link in footnote 1 is now dead. It should probably be repointed at the current book available from
Springer, since the author had pulled all the older copies. Alternatively, some other reference should be used.
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the Schur multiplier is trivial. Robinson's text on group theory contains the following lemma: The Sylow subgroup of the Schur multiplier of a group is a quotient of the Schur multiplier of the Sylow subgroup.
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Okay, thanks for clearing that up. I tend to forget (and then remember, and then forget) the sizes of GL(n,F), PGL(n,F), SL(n,F), and PSL(n,F), and how they depend on whether or not F has a square root of -1.
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Hi all, I would be happy if the article would explain the name 'Alternating' for this group. As long as this is unfortunately not the case, maybe somebody is willing to explain it on this talk page? Regards,
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PGL(2,F_5) has order (5-1)*5=120 and permutes 6 rays. PSL(2,F_5) is the subgroup in PGL(2,F_5) of even permutations, order 60. It permutes 5 of its cosets in A
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has a twofold perfect cover, but it is not SL(4,2)=PSL(4,2)=A8. Until someone salvages the good content, I commented out the text on the article page.
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is a mathoverflow post answering this question. Maybe someone could work this up to a small section on etymology on this wikipedia page?
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I checked the archives, but the referenced work, "Chapter 2: Alternating groups" no longer exists in any of the archives. —
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It may be wise to place in a new section since there is another error making the correct version somewhat irrelevant. A
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The group of scalar matrices in GL(4,2) is trivial, so this is not a way to construct a central extension of A
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and SL(2,9). Take the subgroup consisting of pairs in which both elements correspond to the same element in A
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is confusing to me. Is it because, in the examples that are given, every permutation by which permutation
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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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all have the latter. I shall make the appropriate changes unless there are any objections.
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If you found an error with any archives or the URLs themselves, you can fix them with
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http://web.archive.org/web/20110522121819/http://www.maths.qmul.ac.uk/~raw/fsgs.html
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Since no objections have been raised in the intervening 28 months, go for it. --
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PSL(2,F_4) has order (4-1)*4=60 and permutes 5 rays. Thus it is isomorphic to A
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is not perfect, so it has no universal perfect extension. As you noted, A
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after the link to keep me from modifying it. Alternatively, you can add
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Done! (The roman/upright notation is presumably to distinguish from the
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An editor has reviewed this edit and fixed any errors that were found.
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to keep me off the page altogether. I made the following changes:
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is odd? If so, shouldn't the article mention this explicitly?
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When you have finished reviewing my changes, please set the
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On a slightly more mundane note, this article uses both A
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I have just added archive links to one external link on
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586:{\displaystyle \operatorname {PSL} _{2}(9)\cong A_{6}}
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38:It is of interest to the following
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1094:Mid-priority mathematics articles
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534:{\displaystyle A_{4},A_{5},A_{8}}
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115:Knowledge:WikiProject Mathematics
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700:One affordable reference is (
675:04:51, 16 February 2008 (UTC)
667:Scott Tillinghast, Houston TX
652:Scott Tillinghast, Houston TX
403:Scott Tillinghast, Houston TX
362:03:13, 18 November 2009 (UTC)
265:05:08, 26 December 2007 (UTC)
257:Scott Tillinghast, Houston TX
109:and see a list of open tasks.
384:02:44, 17 October 2007 (UTC)
347:List of finite simple groups
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281:19:06, 4 February 2008 (UTC)
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857:{\displaystyle A_{n}}
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897:{\displaystyle q}
877:{\displaystyle p}
779:Conjugacy classes
763:comment added by
722:978-0-486-65377-8
370:Schur multipliers
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343:group of Lie type
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112:Mathematics
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59:Mathematics
30:Start-class
1083:Categories
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319:Xantharius
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273:John Baez
230:John Baez
1005:Cheers.—
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286:Notation
206:365 days
170:Archives
1066:Zaunlen
1047:Bob.v.R
1015::Online
967:checked
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736:Marvoir
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315:Algebra
311:Algebra
139:on the
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354:nbarth
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