Timeline for Determining the conjugacy classes of a wreath product $G \wr S_n$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 10, 2018 at 12:10 | comment | added | Derek Holt | Sorry $G$ should be $W$. I don't have a $G$. I have $W = A^d \rtimes P$. Of course $P=S_n$ in your question. | |
| Oct 10, 2018 at 12:09 | history | edited | Derek Holt | CC BY-SA 4.0 |
edited body
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| Oct 10, 2018 at 12:07 | vote | accept | Chris Russell | ||
| Oct 10, 2018 at 11:29 | comment | added | Chris Russell | I think I get the idea of how it works now but I'm not sure what $G$ is in the second last paragraph of your updated answer, which is confusing me. In one place I'm interpreting that $A^d$ is a subgroup of $G$ but in another $g \in G$ where I thought $g$ is an element of $P$. | |
| Oct 10, 2018 at 10:49 | history | edited | Derek Holt | CC BY-SA 4.0 |
added 892 characters in body
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| Oct 10, 2018 at 10:48 | comment | added | Derek Holt | My answer was incomplete because it only described the $A^d$-classes. Calculating the $G$-classes from thsi information is not difficult - I have added some further explanation. | |
| Oct 10, 2018 at 9:32 | comment | added | Chris Russell | Thank you Derek, I see how an element $(g, x)$ is conjugate to something in the set $R$ you define. If I write $$R_g := \{\,(g,x) \mid x_i = 1 \ \mathrm{for}\ i \not\in \{r_1,\ldots,r_s\},\, x_i \in \{x^{(1)},\ldots,x^{(k)}\}\ \mathrm{for}\ i \in \{r_1,\ldots,r_s\}\,\}$$ is there a way to describe a subset of $$\bigcup_{g \in G}R_g$$ which contains only one representative from each conjugacy class? Also is there a way to determine how many elements are in a each conjugacy class? | |
| Oct 9, 2018 at 18:12 | history | answered | Derek Holt | CC BY-SA 4.0 |