Timeline for Finite groups with lots of conjugacy classes, but only small abelian normal subgroups?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| May 10, 2016 at 6:58 | comment | added | YCor | These examples have commutator subgroup of bounded size. However, say assuming $q$ is odd, if we allow the 1 in the upper left and lower right to be replaced by $\pm 1$ (so we get a group $\{\pm 1\}^2\ltimes G_n$), the commuting probability is $\ge 1/16q$ and the derived subgroup is the subgroup $G_n$ of index 4, and abelian subgroups have index $\ge q^n$ (probably $\ge 4q^n$). | |
| May 10, 2016 at 6:53 | comment | added | YCor | @YemonChoi: it's extraspecial iff $q$ is prime | |
| May 9, 2016 at 21:04 | comment | added | Yemon Choi | Are these examples of extraspecial $q$-groups? (I had a feeling that they would give a counterexample, but couldn't quite get the right bounds on the index of an abelian subgroup) | |
| May 9, 2016 at 20:24 | vote | accept | Alexander Bors | ||
| May 9, 2016 at 19:54 | history | answered | YCor | CC BY-SA 3.0 |