Timeline for Center of p-groups
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 6 at 14:49 | comment | added | YCor | @ArturoMagidin Ah, I see. I certainly don't have in mind such a narrow notion of central product. I would define it as any quotient of a direct product groups by a central subgroup. | |
| Feb 6 at 14:47 | comment | added | Arturo Magidin | @YCor Not quite (or not always); $G$ is the central product of $H$ and $K$ if and only if $[H,K]=1$, $G=HK$, and $H\cap K=Z(G)$. (E.g., Leedham-Green and McKay, Structure of Groups of Prime Power Order, Definition 2.2.6). This is equivalent to an isomorphism $f\colon Z(H)\to Z(K)$ and taking $H\times K/\{(h,f(h)\mid h\in H\}$. The example does not satisfy the third condition. I think I've seen the third condition relaxed in some places, but it is because of that condition that I did not call it a central product. | |
| Feb 6 at 8:39 | comment | added | YCor | What you call "amalgamated direct product" is often called "central product". | |
| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jul 5, 2016 at 4:35 | comment | added | tj_ | Thank you. So, if I'm not missing something, it is a split metacyclic p-group. | |
| Jul 5, 2016 at 2:07 | comment | added | Arturo Magidin | @tj_: Not off the top of my head, but the description should provide something relatively straightforward. Presumably it is similar to the presentation for regular dihedral groups given as $r^n=s^2=1$, $sr=r^{n-1}s$; but the order of $r$ would be $p^n$, the order of $s$ would be $p$ instead of $2$. | |
| Jul 5, 2016 at 0:25 | comment | added | tj_ | Do you happen to know a presentation of the "dihedral group for odd primes" $\mathbf{E}_{p^n}$ ? | |
| Sep 15, 2012 at 3:56 | history | edited | Arturo Magidin | CC BY-SA 3.0 |
trying to fix the latex in the addition; deleted 9 characters in body
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| Sep 15, 2012 at 0:18 | vote | accept | i. m. soloveichik | ||
| Sep 15, 2012 at 0:15 | vote | accept | i. m. soloveichik | ||
| Sep 15, 2012 at 0:18 | |||||
| Sep 14, 2012 at 20:33 | history | edited | Arturo Magidin | CC BY-SA 3.0 |
add parenthetical comment on index p
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| Sep 14, 2012 at 20:12 | history | edited | Arturo Magidin | CC BY-SA 3.0 |
typos; added 167 characters in body
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| Sep 14, 2012 at 19:57 | history | answered | Arturo Magidin | CC BY-SA 3.0 |