Timeline for For which kinds of group $G$, can we identify a square element efficiently?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 4, 2019 at 1:33 | vote | accept | Licheng Wang | ||
| Apr 4, 2019 at 1:33 | vote | accept | Licheng Wang | ||
| Apr 4, 2019 at 1:33 | |||||
| Apr 4, 2019 at 1:19 | vote | accept | Licheng Wang | ||
| Apr 4, 2019 at 1:21 | |||||
| May 18, 2018 at 18:03 | vote | accept | Licheng Wang | ||
| Aug 14, 2018 at 1:57 | |||||
| May 15, 2018 at 12:27 | comment | added | Geoff Robinson | You need to know the character table of your group, and to be able to calculate the Frobenius-Schur indicators of irreducible characters. By the way, there is an inequality (for finite groups) whose proof by character theory is elementary: if G has s(G) squares and r(G) real-valued irreducible characters, then s(G) is greater than or equal to |G|/r(G). Groups of odd order show that this inequality can't be improved in general, and the inequality is strict infinitely often. | |
| May 12, 2018 at 19:04 | comment | added | Licheng Wang | Is there a method for computing your mentioned formula $\sum_{\chi\in Irr(G)}\mu(\chi)\chi(x)$ efficiently? | |
| May 12, 2018 at 18:45 | comment | added | Geoff Robinson | Most text books on character theory of finite groups cover the Frobenius-Schur indicator ( if you have access to some of these). One such is the book "Character Theory" by I.M. Isaacs. | |
| May 12, 2018 at 18:39 | comment | added | Licheng Wang | Thanks a lot! Would you please suggest me some references for a better study on this topic? In particular, I want to study the case when $G$ is the multiplicative group of the matrix ring $M_d(\mathbb Z_N)$. | |
| May 12, 2018 at 18:35 | vote | accept | Licheng Wang | ||
| May 18, 2018 at 18:03 | |||||
| May 12, 2018 at 18:22 | history | answered | Geoff Robinson | CC BY-SA 4.0 |