Timeline for Group homology for a metacyclic group
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2023 at 12:53 | comment | added | Kasper Andersen | @MikhailBorovoi Yes $\text{tr}$ is short for transfer also known as restriction. | |
| Nov 25, 2023 at 10:19 | vote | accept | Mikhail Borovoi | ||
| Nov 25, 2023 at 10:15 | comment | added | Mikhail Borovoi | Excellent! Many thanks! You write: $$H_k(G,M)\stackrel{\text{tr}}{\rightarrow} H_k(S,M)\stackrel{i_{S,*}}{\rightarrow} H_k(G,M)$$ is multiplication by $[G:S]$. What is $\rm tr$? Is it the restriction map? | |
| Nov 25, 2023 at 10:01 | comment | added | Kasper Andersen | @MikhailBorovoi I replaced the original incorrect argument by a much simpler one. | |
| Nov 25, 2023 at 9:59 | history | edited | Kasper Andersen | CC BY-SA 4.0 |
Corrected wrong argument
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| Nov 24, 2023 at 19:11 | comment | added | Mikhail Borovoi | (cont.) Therefore, the natural homomorphism $H_1(P,M)\to H_1(G,M)$ cannot be surjective. What do you think about this? | |
| Nov 24, 2023 at 19:10 | comment | added | Mikhail Borovoi | The following seems to be a counter-example to your assertion. Let $G={\Bbb Z}/3{\Bbb Z}\times {\Bbb Z}/2{\Bbb Z}$, $M={\Bbb Z}$. Then $$H_1(G,M)\cong G/[G,G]=G={\Bbb Z}/3{\Bbb Z}\times {\Bbb Z}/2{\Bbb Z},$$ whereas $$H_1(P,M)\cong{\Bbb Z}/3{\Bbb Z}/[{\Bbb Z}/3{\Bbb Z}, Z/3{\Bbb Z}]={\Bbb Z}/3{\Bbb Z}.$$ | |
| Nov 24, 2023 at 13:18 | history | edited | Kasper Andersen | CC BY-SA 4.0 |
added 63 characters in body
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| Nov 24, 2023 at 13:11 | history | answered | Kasper Andersen | CC BY-SA 4.0 |