Timeline for Units in group rings.

Current License: CC BY-SA 4.0

15 events

when toggle format	what		by	license	comment
Dec 13, 2018 at 2:23	vote	accept	Fedex
Dec 13, 2018 at 1:29	comment	added	David E Speyer		Regarding the ettiquette question, it is usually better to start a new question which people have put significant effort into the old one. But, in this case, the new condition doesn't help anyway.
Dec 13, 2018 at 1:16	comment	added	David E Speyer		You still lose. $(x^2-x+1) + (x^5+x^4+x^3+x^2+x+1)$ has nonnegative coefficients and acts by $0$ on the same representations as before. In general, replace all occurences of $\Phi_{pq}(g)$ above with $\Phi_{pq}(g) + N (1+x+\cdots + x^{pq})$ where $N$ is sufficiently large and divisible by $\|G\|$.
Dec 13, 2018 at 0:18	comment	added	Fedex		Also, is it ok if I add a note at the end of the original question to add in this condition, or should I just start a new post? I'm not sure what MO etiquette is.
Dec 13, 2018 at 0:13	comment	added	Fedex		Thanks very much for your extremely detailed response! Can I please be annoying and add the condition that $a_1, ... a_n$ is a sequence of non-negative integers? The argument I had in mind in the cyclic case was to construct a polynomial $f(x)$ with coefficients $a_i$ like the one you did ($g^2 - g + 1$), and you'd then have that $f(x)$ divides $g(x) = \frac{x^n-1}{x-1}$. However, as $g(1) = n$ and $f(1)$ is relatively prime to $n$, this is a contradiction -- unless of course $f(1) = 1$ -- and the condition $a_i \geq 0$ deals with that case.
Dec 12, 2018 at 1:49	history	edited	David E Speyer	CC BY-SA 4.0	added 98 characters in body
Dec 12, 2018 at 1:33	history	edited	David E Speyer	CC BY-SA 4.0	added 473 characters in body
Dec 11, 2018 at 17:42	comment	added	David E Speyer		Thank you for the correction! Indeed, $S_3$ does seem to obey this condition.
Dec 11, 2018 at 17:36	history	edited	David E Speyer	CC BY-SA 4.0	deleted 32 characters in body
Dec 11, 2018 at 17:35	comment	added	Jeremy Rickard		Maybe you’re missing some conditions in the edit? $S_3^{ab}\cong C_2$, whose order is not divisible by 3.
Dec 11, 2018 at 17:35	history	edited	David E Speyer	CC BY-SA 4.0	added 890 characters in body
Dec 11, 2018 at 17:27	history	edited	David E Speyer	CC BY-SA 4.0	added 890 characters in body
Dec 11, 2018 at 2:58	comment	added	LSpice		Alternatively, the product of this element with $(g + 1)(g^3 - 1)$ is $0$. (That's probably effectively the same proof in a minor disguise.)
Dec 11, 2018 at 2:30	history	edited	David E Speyer	CC BY-SA 4.0	added 1 character in body
Dec 11, 2018 at 1:58	history	answered	David E Speyer	CC BY-SA 4.0