Timeline for Centralizers in the universal central extensions of the alternating groups?
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14 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Feb 10, 2015 at 18:05 | comment | added | მამუკა ჯიბლაძე | Concerning the motivation - in an answer to the question "third stable homotopy group of spheres via geometry?" I've mentioned work of Igusa from late 70ies which is related | |
| Feb 10, 2015 at 12:56 | review | Close votes | |||
| Feb 10, 2015 at 19:08 | |||||
| Feb 10, 2015 at 11:46 | comment | added | Geoff Robinson | You won't find anything at all interesting by looking at centralizers of elements of odd order. It's rather the opposite of what is asked, but double covers of $A_{n}$ do sometimes occur as involution centralizers in sporadic simple groups, eg the Lyons group Ly has an involution centralizer $\hat{A_{11}}.$ | |
| Feb 10, 2015 at 8:07 | vote | accept | Qiaochu Yuan | ||
| Feb 10, 2015 at 7:51 | answer | added | Dima Pasechnik | timeline score: 2 | |
| Feb 10, 2015 at 7:43 | comment | added | Qiaochu Yuan | @Dima: yes, on second thought, that sounds about right, I think up to a $\mathbb{Z}_2$-central extension and then up to taking a subgroup of index $2$? | |
| Feb 10, 2015 at 7:26 | comment | added | Dima Pasechnik | IMHO the answer to Q1 is no, all these centralisers are boring, and look much the same as these in $A_n$, give or take a central extension of a semidirect product of a bunch of $A_k$ and $S_m$... | |
| Feb 10, 2015 at 7:06 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Feb 10, 2015 at 7:05 | comment | added | Qiaochu Yuan | @YCor: by the centralizer of a conjugacy class I mean the centralizer of an element in that conjugacy class (which is independent, up to isomorphism, of the choice of such an element, so its isomorphism class is a well-defined invariant of the conjugacy class). Sorry if that was unclear. | |
| Feb 10, 2015 at 7:03 | comment | added | YCor | The centralizer of a conjugacy class is a normal subgroup and hence is either $\tilde{A_n}$ or central. I guess it's not what you mean but the formulation is awkward. | |
| Feb 10, 2015 at 6:47 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Feb 10, 2015 at 6:38 | history | asked | Qiaochu Yuan | CC BY-SA 3.0 |