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Results tagged with gr.group-theory
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user 95243
Questions about the branch of algebra that deals with groups.
5
votes
Accepted
Why $G/F(G)$ is isomorphic to a subgroup of ${\rm Out}(F(G))$?
For (2), there is a general construction at work here. Given a short exact sequence of groups
$$1 \to K \to G \to Q \to 1$$
there is always a well-defined homomorphism $\varphi: Q\to \mathrm{Out}(K) …
- 470
18
votes
1
answer
512
views
Can a group have a cyclical derived series?
Given any group $G$, one can consider its derived series
$$G = G^{(0)}\rhd G^{(1)}\rhd G^{(2)}\rhd\dots$$
where $G^{(k)}$ is the commutator subgroup of $G^{(k-1)}$. A group is perfect if $G=G^{(1)}$ …
- 37.4k
12
votes
1
answer
803
views
Does a (nice) centerless group always have a centerless profinite completion?
This is an extension of a question I asked here on Math.SE
Assume that I have a finitely generated residually finite centerless group $G$. Is it true that the profinite completion $\hat{G}$ also ha …
- 63.9k