Timeline for relatively free groups in $Var(S_3)$
Current License: CC BY-SA 4.0
7 events
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| Sep 11, 2018 at 22:22 | comment | added | Arturo Magidin | (cont) where $\mathfrak{A}_2$ is the variety of abelian groups of exponent $2$. But in this case, it just says that the relatively free group of rank $r$ in $\mathrm{Var}(S_3)$ is a subdirect product of the free group of rank $r$ in $\mathrm{Var}(S_3)$ and the $C_2^r$, amalgamating precisely the latter, i.e., it says nothing at all. As far as structure, it further notes that $\mathrm{Var}(S_3) = \mathrm{A}_3\mathrm{A}_2$. This suffices to calculate the size (the objective of the paper), but not to describe the group, I think.... | |
| Sep 11, 2018 at 22:18 | comment | added | Arturo Magidin | @AndrásBátkai: It does not strike me as particularly useful; it states that if you have a dihedral group of order $2^{d+1}e$ with $e$ odd, then you can view it as a subdirect product of a dihedral group of order $2e$ and one of order $2^{d+1}$; if $\mathfrak{U}$ is the variety generated by the first, and $\mathfrak{B}$ the variety generated by the second, and $\mathfrak{V}$ is the variety generated by your original dihedral, then $F_r(\mathfrak{V})$ is "the subdirect product of $F_r(\mathfrak{U})$ and $F_r(\mathfrak{B})$ amalgamating precisely $F_r(\mathfrak{A}_2)$ (cont) | |
| Sep 11, 2018 at 18:00 | review | Late answers | |||
| Sep 11, 2018 at 18:05 | |||||
| Sep 11, 2018 at 17:54 | history | edited | András Bátkai | CC BY-SA 4.0 |
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| Sep 11, 2018 at 17:53 | comment | added | András Bátkai | Would you summarize the contents of the link for those who do not have access? | |
| Sep 11, 2018 at 17:40 | review | First posts | |||
| Sep 11, 2018 at 17:54 | |||||
| Sep 11, 2018 at 17:38 | history | answered | R. Keith Dennis | CC BY-SA 4.0 |