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Results tagged with gr.group-theory
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user 7983
Questions about the branch of algebra that deals with groups.
3
votes
1
answer
411
views
Common supplements to terms of descending central filtrations
Let $G$ be a group and let $(K_n : n \in \mathbb N)$ where $K_n \ne \{e\}$ for all $n$ be a descending central filtration of $G$ with the trivial intersection. Can anyone please give me examples of mo …
- 6,357
5
votes
Accepted
Can all terms of the Johnson filtration be hom-mapped onto the same nontrival group?
The answer seems to be affirmative. We use the idea of Henry Wilton that the image might be taken as an alternating group $A_q$, a simple one (see his comment above). Let $K=\mathcal A(1).$ Then
$\ma …
- 364
5
votes
1
answer
300
views
Can all terms of the Johnson filtration be hom-mapped onto the same nontrival group?
Let $F_n$ where $n \ge 3$ be a free group and let $(\mathcal A_n(k))$ where $k \ge 1$ be the
kernel of the homomorphism $Aut(F_n) \to Aut(F_n/\gamma_{k+1}(F))$
determined by the natural homomorphism $ …
- 364