Timeline for Automorphism group of a finite group
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 23, 2016 at 7:11 | comment | added | yakov | A description of automorphism groups of abelian $p$-groups is nore difficult than the classification of all finite groups. But it is not very difficut to compute the order of an abelian $p$-group of given type. | |
| Oct 17, 2013 at 6:52 | comment | added | Amritanshu Prasad | (continued) In her PhD thesis (imsc.res.in/xmlui/handle/123456789/198), Pooja Singla explains that this extension actually splits (but in general $GL_2(\mathbf Z/p^2\mathbf Z)$ is not a split extension over $GL_2(\mathbf Z/p\mathbf Z)$) citing papers of Sah and Ginosar. | |
| Oct 17, 2013 at 6:44 | comment | added | Amritanshu Prasad | @NickGill $GL_2(\mathbf Z/2\mathbf Z)$ is a quotient of $\mathrm{Aut}(\mathbf Z/4\mathbf Z\times \mathbf Z/4\mathbf Z)$. The kernel is an abelian group isomorphic to the additive group of $2\times 2$ matrices $M_2(\mathbf Z/2\mathbf Z)$. | |
| Oct 16, 2013 at 9:14 | comment | added | Nick Gill | While I'm at it, your first sentence suggests that you might be interested in non-abelian groups also... If this is the case, then Burnside's result on automorphisms of $p$-groups is very useful. (See p.174 of Gorenstein's "Finite groups".) | |
| Oct 16, 2013 at 9:12 | comment | added | Nick Gill | There is something wrong when you write that ``$GL_4(\mathbb{Z})$ should lie in $Aut(\mathbb{Z}/4\mathbb{Z} \times \mathbb{Z}/4\mathbb{Z})$'', because the first is an infinite group! I presume that what you really mean is something like $GL_2(\mathbb{Z}/2\mathbb{Z})$ should lie in $Aut(\mathbb{Z}/4\mathbb{Z} \times \mathbb{Z}/4\mathbb{Z})$(?) | |
| Oct 16, 2013 at 4:34 | comment | added | Arturo Magidin | For general results, see Bidwell, J.N.S., Curran, M.J., and McCaughan, D. Automorphisms of direct products of finite groups, Arch. Math. (Basel) 86 (2006) no. 6, 481-489; and Bidwell, J.N.S. Automorphisms of direct products of finite groups II. Arch. Math. (Basel) 91 (2008) no. 2, 111-121. | |
| S Oct 16, 2013 at 4:05 | history | suggested | Amritanshu Prasad |
added tag "abelian-groups"
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| Oct 16, 2013 at 4:03 | review | Suggested edits | |||
| S Oct 16, 2013 at 4:05 | |||||
| Oct 16, 2013 at 3:42 | answer | added | Amritanshu Prasad | timeline score: 13 | |
| S Oct 16, 2013 at 1:35 | history | suggested | SashaKolpakov | CC BY-SA 3.0 |
edited the English, LaTeX, more tags added
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| Oct 16, 2013 at 1:02 | review | Suggested edits | |||
| S Oct 16, 2013 at 1:35 | |||||
| Oct 15, 2013 at 22:56 | comment | added | Lucia | See this paper msri.org/people/members/chillar/files/autabeliangrps.pdf which I think appeared in the American Math Monthly. | |
| Oct 15, 2013 at 22:45 | review | First posts | |||
| Oct 15, 2013 at 22:56 | |||||
| Oct 15, 2013 at 22:29 | history | asked | Hair80 | CC BY-SA 3.0 |