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Aug
20
comment p-element centralizing a Sylow p-subgroup
Thank you very much =)
Aug
19
comment p-element centralizing a Sylow p-subgroup
@Bungo: What if I have an arbitary set of p-elements. Is the subgroup generated by these p-elements not automatically a p-subgroup?
Aug
19
comment p-element centralizing a Sylow p-subgroup
@ahulpke: I have $P \subseteq \left<P,g\right>$ and $\left<g\right> \subseteq \left<P,g\right>$, right? But that would be true for any $g \in G$. So I always could generate larger $p$-subgroups, for example with 2 different Sylow p-subgroups? So I definitely have something wrong in my understanding. Besides from that I have $\left<P,g\right> = P\left<g\right>$ as $gx=xg$ for all $x \in P$.
Aug
19
asked p-element centralizing a Sylow p-subgroup
Apr
29
comment Image of subgroup under group automorphism lies in itself
Thank you so much! This almost has driven me mad. I also thought of $ \mathbb{Z} $ and $ 2\mathbb{Z} $, but not as subgroups of $ \mathbb{Q} $.
Apr
29
awarded  Scholar
Apr
29
awarded  Supporter
Apr
29
accepted Image of subgroup under group automorphism lies in itself
Apr
29
asked Image of subgroup under group automorphism lies in itself
Dec
10
comment Inner automorphism of a group-ring
When $ u = \sum_{g \in G} r_g g $ then $ \text{supp}(u) = \{ g \in G | r_g \neq 0 \} $.
Dec
9
asked Inner automorphism of a group-ring
Dec
9
comment Two normal subgroups with trivial intersection, one is characteristic, what about the other?
Thank you Dan. I understand it now.
Dec
5
comment Two normal subgroups with trivial intersection, one is characteristic, what about the other?
I'm sorry, but I don't see why $\mathbb{Z} \times 0_{\mathbb{Z}_2}$ is not characteristic. Could you help me?
Dec
5
awarded  Student
Dec
5
comment Two normal subgroups with trivial intersection, one is characteristic, what about the other?
Because the statement would be a lot stronger if that wasn't needed.
Dec
5
asked Two normal subgroups with trivial intersection, one is characteristic, what about the other?