Timeline for Group action w.r.t. non-split extension group of the form $2^8\mathbin.(2^7\mathbin:\operatorname{Sp}(6,2))$
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Aug 29, 2021 at 7:50 | vote | accept | Isaac | ||
| Nov 9, 2019 at 23:35 | comment | added | LSpice | @DerekHolt, thanks! | |
| Nov 9, 2019 at 22:53 | comment | added | Derek Holt | @LSpice It's known as the ATLAS notation for group structures defined in the Atlas of Finite Groups. Yes, $2^8$ denotes an elementary abelian group. The cyclic group of that order would be denoted by $256$. You can also use $[256]$ to denote a group of that order with unspecified structure. | |
| Nov 9, 2019 at 14:52 | comment | added | LSpice | Where are these various kinds of notations for extensions (the colon and dot, as well as, e.g., whether $2^8$ means, say, the elementary Abelian 2-group of order $2^8$, as I assume, or a cyclic group of order $2^8$, or whatever else) defined? | |
| Nov 9, 2019 at 14:50 | history | edited | LSpice | CC BY-SA 4.0 |
TeX fixes
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| Nov 9, 2019 at 13:35 | comment | added | David Roberts♦ | @Isaac en.wikipedia.org/wiki/Outer_automorphism_group See also the top of the second page here: projecteuclid.org/download/pdf_1/euclid.bbms/1102715061. See the classic reference jstor.org/stable/1969174 and the discussion and references at encyclopediaofmath.org/index.php/Extension_of_a_group | |
| Nov 9, 2019 at 13:12 | answer | added | Derek Holt | timeline score: 4 | |
| Nov 9, 2019 at 9:20 | history | edited | Dima Pasechnik | CC BY-SA 4.0 |
texification and no greetings
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| Nov 9, 2019 at 8:41 | history | edited | Isaac | CC BY-SA 4.0 |
added 62 characters in body
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| Nov 9, 2019 at 8:22 | comment | added | Derek Holt | It is not possible to answer this question without further information. There is more than one isomorphism type of group that fits that description. | |
| Nov 9, 2019 at 5:15 | comment | added | Isaac | Can you explain "an outer action of H". | |
| Nov 9, 2019 at 4:29 | comment | added | David Roberts♦ | You might wish to consider the general case of $G.H$ — $G$ is a normal subgroup of $G.H$, so $G.H$ acts by conjugation. From this you can achieve an outer action of $H$. | |
| Nov 9, 2019 at 3:23 | history | edited | Isaac | CC BY-SA 4.0 |
edited body; edited title
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| Nov 8, 2019 at 19:59 | comment | added | Derek Holt | Also the title of your post does not agree with the body. | |
| Nov 8, 2019 at 18:37 | comment | added | verret | Assuming this is usual Atlas notation, $2^8$ does not act on $(2^7:Sp(6,2))$, since the latter is a quotient, not a normal subgroup. | |
| Nov 8, 2019 at 17:34 | history | edited | YCor |
edited tags
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| Nov 8, 2019 at 17:00 | review | Close votes | |||
| Nov 16, 2019 at 3:05 | |||||
| Nov 8, 2019 at 16:05 | review | First posts | |||
| Nov 8, 2019 at 16:41 | |||||
| Nov 8, 2019 at 16:01 | history | asked | Isaac | CC BY-SA 4.0 |