Timeline for Is $\mathbb{Z}_p$ flat $\mathbb{Z}_pG$-module for a finite $p$-group $G$?

11 events

when toggle format	what		by	license	comment
S Jul 5, 2011 at 8:19	vote	accept	qkqh
Jul 5, 2011 at 8:19	vote	accept	qkqh
S Jul 5, 2011 at 8:19
Jun 27, 2011 at 21:10	history	edited	Ralph		edited tags
Jun 27, 2011 at 21:00	answer	added	Ralph		timeline score: 7
Jun 27, 2011 at 16:11	answer	added	Mariano Suárez-Álvarez		timeline score: 3
Jun 27, 2011 at 14:25	answer	added	JSE		timeline score: 4
Jun 27, 2011 at 8:36	comment	added	qkqh		@Mariano Suárez-Alvarez : I used a (augmented) free resolution $\cdots \to \mathbb{Z}_{(p)}G \to \mathbb{Z}_{(p)}G \to \mathbb{Z}_{(p)}G (\to \mathbb{Z}_{(p)} \to 0)$ such that first map sends $g$ to $1$, second sends $g$ to $g-1$, (last one is the augmentation map) and the fore two maps are repeated. Then by tensoring $\mathbb{Z}_{(p)}$, $\cdots \to \mathbb{Z}_{(p)} \to \mathbb{Z}_{(p)} \to \mathbb{Z}_{(p)}$ is obtained wih identity map and zero map. And I guess it is similar when $G$ is another finite $p$-group. Does this have wrong parts?^^;;
Jun 27, 2011 at 8:14	comment	added	qkqh		@Mariano Suárez-Alvarez : Isn't $\operatorname{Tor}_^{\mathbb{Z}_{(p)}G}(\mathbb{Z}_{(p)},\mathbb{Z}_{(p)})=0$ for $\neq 0$? when $G=\mathbb{Z}/p\mathbb{Z}$
Jun 27, 2011 at 5:56	comment	added	Mariano Suárez-Álvarez		(Try it with $G$ the cyclic group of order $p$ first)
Jun 27, 2011 at 5:42	comment	added	Mariano Suárez-Álvarez		Can you compute $\operatorname{Tor}^{\mathbb Z_{(p)}G}_\bullet(\mathbb Z_{(p)},\mathbb Z_{(p)})$ ?
Jun 27, 2011 at 5:31	history	asked	qkqh	CC BY-SA 3.0