Timeline for Characterization of the transfer map in group theory
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 18, 2011 at 18:44 | comment | added | Benjamin Steinberg | In fact, my answer is in some sense equivalent to Geoff's. Huppert and Wielandt observed that the Krasner-Kaloujnine embedding can be viewed as a representation by monomial matrices over H. This representation they observe is none other than the induced rep Geoff discusses. This is why I said along the lines of Geoff. | |
| Dec 18, 2011 at 18:28 | comment | added | Benjamin Steinberg | Also Geoff's answer has the same defect because one first chooses a basis to define determinant and then shows independence of the basis. This can be disguised using exterior powers but it is still there. | |
| Dec 18, 2011 at 18:22 | comment | added | Benjamin Steinberg | Perhaps Sylvain's article gets around the choice (I haven't read it yet)? The choice inner automorphism is uniquely determined by the change in transversals which is why there might be a 2-category explanation. | |
| Dec 18, 2011 at 18:02 | comment | added | Martin Brandenburg | @Sylvain: Thanks for the reference, this is a very interesting article. It illustrates how natural some ad hoc constructions are when we consider them via (higher) categories. @Benjamin: So the embedding depends on a choice and after all you prove that it is independant from it. But thus is exactly what I would like to avoid. I don't think that your answer (though the content interesting for itsself) answers my question. | |
| Dec 18, 2011 at 15:28 | comment | added | Sylvain Bonnot | The article "Embedding into wreath product and the Yoneda lemma" seems to do what you mentioned... I found it there: kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1318-18.pdf | |
| Dec 18, 2011 at 15:08 | comment | added | Benjamin Steinberg | By the way, I would like a categorical interpretation of the Krasner-Kakoujnine embedding. Maybe one needs 2-categories since it is defined up to inner automorphism. | |
| Dec 18, 2011 at 15:06 | history | answered | Benjamin Steinberg | CC BY-SA 3.0 |