Timeline for The probability that two elements of a finite nonabelian simple group commute
Current License: CC BY-SA 4.0
3 events
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| Sep 19, 2018 at 10:48 | comment | added | Geoff Robinson | Note that Dixon's argument can be simplified a little. No finite simple group can have an irreducible complex character of degree $2$. If $G$ were a simple group with such a representation, then $|G|$ would be even (since irreducible character degrees divide the group order). Then $G$ would contain an involution $t$ by Cauchy's theorem, and $t$ would be in $Z(G)$ since $t$ would be represented by $-I$ (on consideration of determinant), contrary to simplicity. | |
| Sep 19, 2018 at 6:58 | history | edited | YCor | CC BY-SA 4.0 |
Added reference info, will help in case link is broken.
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| Sep 19, 2018 at 3:45 | history | answered | Keith Kearnes | CC BY-SA 4.0 |