Timeline for Character tables and simple groups.
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 11, 2016 at 10:14 | comment | added | Frieder Ladisch | @FarrokhShirjian: Thank you very much for your comment, I have edited to clarify and to incorporate your useful information. I silently assumed "in the class of finite simple groups" since the question asked for two simple groups with the same character table. | |
| Jan 11, 2016 at 10:09 | history | edited | Frieder Ladisch | CC BY-SA 3.0 |
Clarified, added information from comment
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| Jan 2, 2016 at 20:18 | comment | added | Farrokh Shirjian | In fact it would be better to say that " By the result of Landazuri et al, a finite simple group is determined by its irreducible character degrees (counting multiplicity) in the class of finite simple groups..." | |
| Dec 29, 2015 at 16:36 | comment | added | Farrokh Shirjian | More evidence: Let $S$ be a finite simple group and $G$ a finite group such that $S$ and $G$ have the same irreducible character degrees (counting multiplicities). Then we have the isomorphism $\mathbb{C}S \cong \mathbb{C}G$ of their complex group algebras, and it was not until 2012 that Tong-Viet in a serie of papers proved that in this situation $S \cong G$. (See Theorem 1.1 of "Simple classical groups of Lie type are determined by their character degrees. Journal of Algebra (357) (2012)" | |
| Dec 29, 2015 at 16:29 | comment | added | Farrokh Shirjian | Sorry, but I think something is not true in your answer. By the time before 2000s, the problem of characterizing finite simple groups with their irreducible character degrees (with multiplicities) was open. So It could not be deduced from the result of Lanadzuri et al. | |
| Mar 9, 2011 at 11:08 | history | edited | Frieder Ladisch | CC BY-SA 2.5 |
deleted 52 characters in body
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| Mar 5, 2011 at 12:48 | history | answered | Frieder Ladisch | CC BY-SA 2.5 |