Timeline for Relation between the genus number and the ambiguous class number
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 22 at 17:39 | comment | added | A. Maarefparvar | @FranzLemmermeyer Thanks again for giving another example for F=Q. But, what happens if we replace ambiguous ideal classes with "strongly" ambiguous ones? In other words, conjecturally, it seems that "For an imaginary abelian number field K, the number of strongly ambiguous ideal classes in K divides the genus number of K." For instance, in your second example, the genus number is 1 and the group of strongly ambiguous ideal classes in K is also trivial. | |
| Aug 22 at 17:31 | vote | accept | A. Maarefparvar | ||
| Aug 22 at 16:46 | comment | added | Franz Lemmermeyer | $[2,2]$ is short for the direct sum of two groups of order $2$. | |
| Aug 22 at 14:51 | vote | accept | A. Maarefparvar | ||
| Aug 22 at 17:31 | |||||
| Aug 22 at 9:14 | comment | added | user267839 | a silly question: what means the notion $[2,2]$ encoding "type" of a class group? (How to interpret it? Sorry, if it's standard, haven't seen it before) | |
| Aug 22 at 7:54 | history | edited | Franz Lemmermeyer | CC BY-SA 4.0 |
added 401 characters in body
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| Aug 21 at 17:37 | comment | added | A. Maarefparvar | Thanks for providing this counterexample. But, how about if we restrict the assumptions to "F=Q and K is an imaginary abelian field"? | |
| Aug 21 at 6:55 | history | answered | Franz Lemmermeyer | CC BY-SA 4.0 |