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Results tagged with gr.group-theory
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user 22088
Questions about the branch of algebra that deals with groups.
2
votes
Is the intersection of two subgroups, defined below, always trivial?
As pointed out, the Kervaire conjecture requires an assumption about the exponent sum on $g$. So, in fact, the answer to the original question is"no".
Take $H$ be the cyclic group of order 6 generate …
- 101
1
vote
An endomorphism of free groups
Another argument:
As said above, it suffices to show that the subgroup $S=<\{g_i \alpha_i g_i^{-1}\}>$ has rank $n$. We make the subgroup graph $\Gamma_S$ of $S$ by identifying at a basepoint the roo …
- 101
-1
votes
A subgroup of corank 1 in a free group contains a primitive element?
Assuming $x_1 \notin H$, we can construct a basis for F as follows:
for each j,
if $x_j \notin H$, we set $b_j=x_j$ (in particular, $b_1=x_1$);
if $x_j \in H$, set $b_j=x_1x_j$.
Then, $B=\{b_1, …
- 101