Timeline for Textbook source for finite group properties deducible from character table?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2016 at 12:13 | review | Suggested edits | |||
| Jun 19, 2016 at 12:42 | |||||
| Jun 3, 2012 at 22:33 | comment | added | Anvita | @Jim: In this book, Karpilovsky gives a proof following "an argument due to Isaacs (1976)" referring to the book M.I.Isaacs, Character Theory of Finite Groups, Academic Press, New York-San Fransisco- London. 1976. There is ineed such a proof in Isaacs' book (see chapter on Brauer's theorem there, Theorem (8.21) ) attributed to G.Higman, but no explicit reference given. | |
| May 24, 2012 at 15:41 | comment | added | Jim Humphreys | @Anvita: Do you know where the result quoted by Karpilovsky comes from? His books mostly consisted of compilations from research papers by other people, and I suspect one of these would be the original source. | |
| May 23, 2012 at 12:50 | comment | added | Nick Gill | This is slightly off-topic but, to clarify Anvita's comment: In a finite group $G$, an element $g$ is a commutator if and only if $$\sum\limits_{\chi \in Irr(G)} \frac{\chi(g)}{\chi(1)}\neq 0.$$ This result is stated in the paper by Liebeck, O'Brien, Shalev and Tiep which proves the Ore conjecture; they remark that it follows from a result of Frobenius (see Lemma 2.5 of that paper). | |
| May 22, 2012 at 4:54 | history | answered | Anvita | CC BY-SA 3.0 |